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Thorur has the Endurance Feat and does not take Fatigue for Forced March. He can also cast Create Water and Guidance at will, subject to GM's discretion for the later, of course.
Components: V, S Range: close (25 ft. + 5 ft./2 levels) Effect: up to 2 gallons of water/level Duration: instantaneous Saving Throw: none Spell Resistance: no Description: This spell generates wholesome, drinkable water, just like clean rain water. Water can be created in an area as small as will actually contain the liquid, or in an area three times as large—possibly creating a downpour or filling many small receptacles. This water disappears after 1 day if not consumed. Note: Conjuration spells can't create substances or objects within a creature. Water weighs about 8 pounds per gallon. One cubic foot of water contains roughly 8 gallons and weighs about 60 pounds.
Would like to cast Guidance on everyone "Before they attempt a roll" including Gillie's climb check, as a default action, if allowed, to save time/posts.

GM Losonti |

Hills require 4, not 3. That was a typo that I didn't catch, sorry. The cache is in the tile you're in and is conveniently on the way no matter which direction you head, so it does not add any time to your journey. And while a 12 (with the +1 from Thorur's guidance) is a failure, it's not a critical failure so it doesn't hurt the group as a whole. Also, from double-checking the rules I'm given for the race, there does not appear to be a limit on how many attempts each player can make, beyond the advantage limit given for the terrain. So you could try another one if you wanted. Climb probably won't work again in this phase, though.
Thorur: I think you can still take damage from a Forced March, you just get a +4 on the check to avoid the nonlethal damage (and thus the fatigue from it). Create Water is great, I doubt drinking water will be a problem for the group at all. Casting guidance repeatedly I think we'll treat like the Recovery tactic. It's not so taxing that you couldn't do something else, but any checks you make to gain an advantage while doing that will be at a -5.
Bahram does his best to range ahead and pinpoint easier climbing routes for the rest of the party, but in his zeal it turns out that he missed other, easier paths and so winds up wasting a fair amount of his time.

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Well, in that case...
On his way down from his failed vantage hike, Bahram takes another look around to see what he can Know the area.
Kn. nature: 1d20 + 7 + 2 ⇒ (20) + 7 + 2 = 29

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Sorry. Got a bit ahead of myself with the numbers. DC is listed as 10 or 15. Thorur has 8 plus 4 from Endurance (possible +1 from Guidance). Not guaranteed but pretty close. That's what I ment.
I don't understand why Guidance (+1) would cause a -5 penalty, but if so it would be best if I don't use it.

GM Losonti |

Because it's taking a fair amount of your focus to cast it over and over again for hours at a time. The -5 would only apply to advantage checks made by you specifically during this phase, though.

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Gillie giggles when Bahrain tries to climb a tree.
”Don’t worry! I’ll describe it to you!”
Climb check: 1d20 + 21 ⇒ (18) + 21 = 39
You see as the monstrous claws of his third arm dig into the bark and he can hang from the muscular limb effortlessly.
He then proceeds to describe the countryside in enthusiastic detail.
[ooc] I don’t know how it could work but Gillie weighs bugger all without gear... could he get a piggyback ride? [ooc]

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Yates stares up at the ratfolk in the tree then the sheer cliff face right next to it that reaches halfway up the towering tree. "Gillie! You have some rope in your pack right? Toss it down and I think we could all get over this cliff face with no troubles!"
No more advantage tries right? I think we should look at making gear in the next one if we can.
As he waits for the rope, Yates checks his race sandals, ensuring the odd mental connection he always feels with his implements is there, and then checking his compass once as well just in case.

GM Losonti |

You can attempt as many as you like, but you can only achieve three of them for this phase. Someone could also Craft/Modify Tools or Gather Supplies. You have a +2 bonus on those from your research leading up to the race, though it does reduce your personal progress by half (rounded down), which would slow the group's base progress from 2 to 1.
The upside of Bahram's time spent on looking for shortcuts is that it offers him a great view of the surrounding terrain. Between that and Gillie's better luck at finding easier climbing routes, the team makes excellent progress.
A few hours after the race's start, you arrive at the location marked on the map. The cache is remarkably easy to find, buried in a shallow pit and marked by a stake with a piece of red cloth tied to it. A short dig later, you extract a large chest from the soft sand.
Inside the chest, you find the following:
Six potions of cure light wounds
Four flasks of alchemist's fire
Two suits of masterwork studded leather armor
Two masterwork longbows with 40 arrows
Two masterwork longswords
A quarterstaff
A spell component pouch
Twelve trail rations
Six waterskins
Seven tindertwigs
A wand of cure light wounds with 20 charges
Finally, a traveling spellbook with the following spells:
All wizard cantrips
1st: alarm, burning hands, chill touch, color spray, mage armor, magic weapon, sleep, and true strike
2nd: acid arrow, blur, bull’s strength, daze monster, false life, protection from arrows, scorching ray, and see invisibility
After inventorying and doling out your find, it is time to begin the second phase of the day.

GM Losonti |

Kicking myself for not asking this earlier, but also: where to next?

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Just so we have a reference on the new page:
Hills (Progress 4, Advantages 3)
Jungle (Progress 8, Advantages 8)
Mountains (Progress 6, Advantages 6)
Plains (Progress 2, Advantages 0)
Swamp (Progress 4, Advantages 3)
I added some red arrows to the hex grid that seems to be our shortest rout to the finish line!
Reillana focuses on her magical needs, gathering herbs and reagents so that she and Bahram aren't forced to deplete Bahram's spell component pouch immediately if there's trouble.
Knowledge (Nature): 1d20 + 10 ⇒ (8) + 10 = 18

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Khāṇa keeps an eye out for shortcuts...
Inspired Perception: 1d20 + 9 + 1d6 ⇒ (2) + 9 + (3) = 14 *CRINGE*
...and while not much good comes of that...
Inspired Acrobatics: 1d20 + 5 + 1d6 ⇒ (15) + 5 + (1) = 21 Am I doing this right?
...she proves more adroit at skipping and sliding across the hilly terrain.

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Thorur tries to help the group recognize and evade hazards along the way...
Survival (untrained): 1d20 + 2 ⇒ (11) + 2 = 13
...and will pay close attention to his companions for possible injuries and fatigue.

GM Losonti |

Need to know where you're going first, since the tile you're entering sets the DCs and advantages available.

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I would agree with the 'red route' suggested. Should be the easiest DC's, and smoothest path.
As I usually fill the role of a front line fighter, Bahram would probably vie for the longsword and armor. However, i see that a couple of you have many more hp than me, so I could try my hand at the bow, or be a secondary fighter with the staff. We can each carry a clw pot. I could also be the clw wand monkey.

GM Losonti |

I added an extra step to the route, because while the finish line's point on the map is on a hex corner (for some reason), it actually does lie within that swamp tile so the scenario requires you to enter it. So, taking that route will take you into the next tile.
While the party moves along, Eòshli focuses on gathering spell components and herbs along the route. While this slows the group down, she is able to scrounge up enough ingredients to approximate a spell component pouch. Unfortunately, Thorur leads the group down what he initially believes to be a shortcut, but it dead ends and requires some amount of doubling back to find the path again. Fortunately, Khāṇa spots an easier path up from the dead end and the party doesn't lose too much time from the misadventure.
Summary: Eòshli's Gather Supplies reduces her personal progress (and the group's) to 1, Thorur's critically failed Survival check reduces the group's progress by 1 to 0. Khāṇa's initial failed Perception check reduces her personal progress to 2, which has no effect on the group as a whole, but her successful Acrobatics check increases the group's progress back to 1. The party can still gain 2 advantages for this phase, but we'll get to that in a bit.
Once you're back on track, you take a quick look around. Hogback ridges running east to west stretch as far as the eye can see. The northern slopes of these outcrops are covered by short green grass swaying in the wind, while the southern slopes are steeper and rockier. The sun is just barely peeking out from the clouds, and a gentle breeze carries the scent of the sea. Around the corner and out of view, you can hear what sounds like a group of animals fighting over something.
Please arrange yourselves on Slide 6, and assign the gear as you see fit. I'll start the encounter later tonight.

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Thorur would prefer a longsword and one of the armors, but just the longsword will be fine. He still has his dagger, but is not designed for ranged attacks at all. I think giving Eoshli one of the bows is a no-brainer.
Upon hearing the sounds, Thorur calls out..."Oh great Trudd, please bless your servant with your divine protection."
Please note that Thorur has the Combat Reflexes feat and the Armor Expert trait.
Current AC=12/12/11 not counting possible +3 for the studded leather armor.

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I have my kunai, and can't use the longswords or longbows (at least, not well :P), but I would like one of the studded leathers; I'll also take one or two of the alchemist's fires.

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I don’t want to force a retcon but we already have two spell component pouches,
I snuck one in and we just found a second...
However I was about to suggest we scavenge a rope from the vines so that’s a decent alternative.
As the party starts dealing out the weapons Gillie gets his tailblade out and straps it on.
"This is the only blade I need! It'd be too tricky to make that amour fit me and l'm pretty good at getting out of the way anyway!"
Gillie is a natural attack build and with high dex can do without armour
While the others get into their new armour Gillie takes the time to refill the pit with the sand and tries to disguise their presence as much as possible.

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Yates looks at the armor with a longing look, "I could use one of those. But otherwise I don't need anything from there, other than maybe a potion." As the group is climbing the mountains Yates looks for a good think walking stick that he might be able to use as a weapon in case things come to that.
Perception: 1d20 + 4 ⇒ (10) + 4 = 14

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Based on requests, and my keen observational skills, here is my take on the loot:
Thorur, mw longsword, 1 clw pot
Khana: mw studded leather, 2 alch fire, 1 clw pot
Gille: 1 clw pot, 1 alch fire
Yates: mw studded leather, 1 clw pot
Bahram: mw longsword, mw longbow, 1 clw pot, 1 clw wand
Eoshli: mw longbow, 1 clw pot, staff, 1 alch fire
If someone else wants my bow or wand, I'm fine with that. Eoshli, if you don't want the staff, we can just carry it. The tinder twigs, rations, and waterskins can just be carried as well. I think that's it.

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Yates stated he was looking for a walking stick that can be used as a possible weapon. Pretty sure the staff fits that description.

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Yates runs purely on Improvised Weapons, making good use of them and increasing the damage die by two steps. An actual weapon is actaully worse in his hands.

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"Would you like a tree branch?"
Gillie scampers up a tree and looks for a decent sized dead branch to break off for Yates.
I'm happy with that distribution

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Pulling back the bowstring to test its draw, Eoshli smiles to herself. "It's been forty years since I've used a bow in earnest, but some skills are never fully forgotten..."
Sounds good to me, Bahram: mw longbow, 1 clw pot, staff, 1 alch fire for Eoshli
As the sounds of squabbling animals comes their way, Eoshli quirks one eyebrow. "Seems like the locals have a sense of dramatic timing. Is it trouble?"

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"Would you like a tree branch?"
Gillie scampers up a tree and looks for a decent sized dead branch to break off for Yates.
"Oh yes, a tree branch would be extremely useful!" Yates stands below the tree and tries to catch anything that the little one might drop down.

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Yates enthusiasm galvanises Gillie. He works on a selection of branches and even climbs back down for one of the longswords if he can’t break them off by hand

GM Losonti |

As Thorur and Yates round the corner and climb the slope, they see a trio of large, winged lizards fighting over a kill. One of them holds it in its mouth, while the other two try to jump and snatch it for themselves. Upon catching sight of the party, however, they immediately stop fighting, and the first one drops its prey out of its mouth, a small humanoid corpse. With an excited screech, they begin slithering and clawing toward you!
Bahram: 1d20 + 1 ⇒ (18) + 1 = 19
Eòshli: 1d20 + 7 ⇒ (19) + 7 = 26
Yates: 1d20 + 2 ⇒ (4) + 2 = 6
Thorur: 1d20 + 1 ⇒ (16) + 1 = 17
Gillie: 1d20 + 5 ⇒ (15) + 5 = 20
Khāṇa: 1d20 + 1 ⇒ (20) + 1 = 21
Red: 1d20 + 6 ⇒ (7) + 6 = 13
Blue: 1d20 + 6 ⇒ (1) + 6 = 7
Green: 1d20 + 6 ⇒ (15) + 6 = 21
Round 1
Eòshli
Green
Khāṇa
Gillie
Bahram
Thorur
Red
Blue
Yates
Eòshli is up first!
If your result was 18 or higher, open the next spoiler.

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Knowledge Arcana: 1d20 + 8 ⇒ (14) + 8 = 22
Yates freezes as he spots the lizards. Fight or flight response getting sublimated into a frenzied evaluation of the lizards instead.

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Knowledge (Arcana): 1d20 + 10 ⇒ (20) + 10 = 30
"Amphipteres, luckily young ones," Eoshli informs the others, pushing forward to get a clear shot. "Be careful, their tails can hook you and they reach much further than than you might expect."
Staring down the nearest of the dragonlike beings, the elf curses them with ill fortune in battle.
Move, then Evil Eye to apply -2atk for 3 rounds (Will15 reduces to 1 round)

GM Losonti |

Green tail vs Yates: 1d20 + 8 ⇒ (17) + 8 = 25
Damage: 1d6 + 2 ⇒ (6) + 2 = 8
The mind of Eòshli's target becomes clouded as her hex takes hold, but one of the other wyrmlings throws itself into the air with its claws and hurtles toward Yates, lashing out and stabbing him with its barbed tail.
Round 1
Eòshli
Green Amphiptere
Khāṇa
Gillie
Bahram
Thorur
Red Amphiptere
Blue Amphiptere -2 to attack for 7 rounds
Yates -8 HP
Yates takes 8 damage from the tail attack. Khāṇa, Gillie, Bahram, and Thorur are up!

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Thorur mutters unpleasant under his breath in the Dwarven tongue, casts a spell, A floating Warhammer of pure force comes in to being next to one of the creature. Thorur then moves forward to help protect Yates.
Warhammer vs. Red: 1d20 + 3 + 2 ⇒ (1) + 3 + 2 = 6
possible Force damage vs. Red: 1d8 + 1 ⇒ (5) + 1 = 6
Just a thought, since we heard them, are we assumed to have drawn weapons? My BAB so I can draw as I move, but was curious about the others.

GM Losonti |

That's fine, though I think everyone in the party has at least +1 BAB so it's probably a moot point.

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Knowledge (Arcana): 1d20 + 3 ⇒ (4) + 3 = 7
Counting herself fortunate to be unfamiliar with these things under the circumstances, Khāṇa warily circles in and takes a jab with her trusty kunai.
masterwork kunai vs Lime: 1d20 + 5 ⇒ (12) + 5 = 17
damage: 1d4 + 2 ⇒ (4) + 2 = 6

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Bahram moves up the trail 15'so that he can see past his comrades.
Ranged has never been my thing. Don't make a full of yourself. More importantly, don't get eaten!
Bahram takes aim at red and lets fly, right into the woods!
mw longbow: 1d20 + 3 ⇒ (6) + 3 = 91d8 ⇒ 3

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Yates gives a start as the ampithere stab him with his tail. He snaps out of the analytic mode and realizes that Eoshili recalled the same information that he did, and spouted it off before the Yates had the chance. "Yup beware the tails! They hurt."
Sorry I've been warned for giving information before my character had initiative.

GM Losonti |

Damage: 1d6 + 2 ⇒ (4) + 2 = 6
Through bad luck, Thorur's warhammer springs into existence just as the dragonkin prepares to throw itself into the air, inadvertently dodging both the swing and an arrow from Bahram.
Khāṇa steps in to deliver a well-aimed strike with her kunai, but the beast's tail snaps around and scores its own hit on the half-orc. Striking for 6 damage.
Round 1
Eòshli
-6 HP
Green Amphiptere
Khāṇa -6 HP
Gillie
Bahram
Thorur
Red Amphiptere -2 to attack for 7 rounds
Blue Amphiptere
Yates -8 HP
Gillie is still up! And no worries Yates. You technically can't make a knowledge check until its your turn, so you made the right call.

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I'm a little confused, is green flying or on the ground.

GM Losonti |

They have a weird movement, they jump up and glide. This gives them a fly speed but they don't actually fly.

GM Losonti |

Delaying Gillie to the next initiative block.
Tail damage: 1d6 + 2 ⇒ (6) + 2 = 8
Blue tail vs Bahram: 1d20 + 8 ⇒ (16) + 8 = 24
Tail damage: 1d6 + 2 ⇒ (6) + 2 = 8
The two other amphipteres throw themselves into the air and glide toward Thorur and Bahram. While Thorur's armor easily deflects the barbed tail, Bahram is less lucky and is struck painfully by his attacker.
Round 2
Gillie
Yates -8 HP
Eòshli
Green Amphiptere -6 HP
Khāṇa -6 HP
Bahram -8 HP
Thorur
Red Amphiptere -2 to attack for 6 rounds
Blue Amphiptere
Bolded characters are up!

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Did Yates get a good stick for whacking things? Something like a quarterstaff?
Yates raises up the branch in his hands by the far end, it's weight causing him to have to shift to one foot, making him look like the epitome of an untrianed combatant on the verge of losing their balance. He stays in the pose, however, constantly seeming to hover on the brink of toppling over, the weight of the branch the only thing keeping him from doing so. After a second or two, he starts moving into action, half tottering, half toppling forward, as he brings the branch around, using the full weight of his body nearly toppling over to drive the impact of the weapon even further.
Ahh! Back foul beast! (Improvised weapon): 1d20 + 6 ⇒ (13) + 6 = 19
Damage (if counts as a quarter staff), Shikigami Style and Mimicry, two handed: 2d6 + 4 ⇒ (1, 4) + 4 = 9

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Sorry, kids first day back at school today after holidays do things were chaotic finding uniforms and lunchboxes and the like. I should have said.
Gillie runs forward and claws at the creature.
Attack: 1d20 + 8 ⇒ (3) + 8 = 11

GM Losonti |

Yates: You're good. And no worries, Gillie, it happens.
Green tail vs Khana: 1d20 + 8 ⇒ (13) + 8 = 21 Hit
Tail damage: 1d6 + 2 ⇒ (6) + 2 = 8
Green bite vs Gillie: 1d20 + 7 ⇒ (8) + 7 = 15 Miss
Bite damage: 1d6 + 2 ⇒ (5) + 2 = 7
Grab: 1d20 + 11 ⇒ (6) + 11 = 17
Constrict: 1d6 + 2 ⇒ (6) + 2 = 8
Wing 1 vs Gillie: 1d20 + 2 ⇒ (15) + 2 = 17 Hit
Wing damage: 1d3 + 1 ⇒ (3) + 1 = 4
Wing 2 vs Yates: 1d20 + 2 ⇒ (4) + 2 = 6 Miss
Wing damage: 1d3 + 1 ⇒ (2) + 1 = 3
Yates's unusual style serves him well, and he is able to deliver a solid blow to the amphiptere. Gillie's attack is less successful, as she dodges its snapping jaws but gets clocked by one of its wings. The creature, realizing it is almost surrounded, begins to panic and attack everything around it. Khāṇa takes the worst of it, as the amphiptere's tail once again finds its mark. 8 damage to Khāṇa and 4 damage to Gillie.
Round 2
Gillie -4 HP
Yates -8 HP
Eòshli
-15 HP, AC hexed for 6 rounds
Green Amphiptere
Khāṇa -14 HP
Bahram -8 HP
Thorur
Red Amphiptere -2 to attack for 6 rounds
Blue Amphiptere
Bolded characters are up!

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Bahram looks down at the puncture in his side and instinctively begins to drop the bow, draw the sword, and advance.
I got hurt! Bad. I've never been hurt bad before. Have I?
Seeing the blood flow out of his unarmored body, he takes a step back and fires his bow again.
longbow: 1d20 + 3 ⇒ (3) + 3 = 61d8 ⇒ 8

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Sorry, kids first day back at school today after holidays do things were chaotic finding uniforms and lunchboxes and the like. I should have said.
Ah yes, this year's new uniforms...!
Khāṇa makes a noise like a diseased crocodile in heat, then makes a careful attempt to retaliate.
masterwork kunai, flank, fighting defensively vs Lime: 1d20 + 3 ⇒ (10) + 3 = 13
damage: 1d4 + 2 ⇒ (2) + 2 = 4

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Thorur moves forward, mutters..."Trudd, please heal your servant's companion."....and touches Khana....
CLW vs. Khana: 1d8 + 3 ⇒ (5) + 3 = 8
Dropping Sanctuary for CLW
...as the magical warhammer continues to attack....
Warhammer vs. Red: 1d20 + 3 + 2 ⇒ (18) + 3 + 2 = 23
possible Force damage vs. Red: 1d8 + 1 ⇒ (3) + 1 = 4

GM Losonti |

Khāṇa, do you have 3 ranks in Acrobatics?
Damage: 1d6 + 2 ⇒ (2) + 2 = 4
Green AoO tail vs Thorur, soft cover: 1d20 + 8 - 4 ⇒ (19) + 8 - 4 = 23
Damage: 1d6 + 2 ⇒ (6) + 2 = 8
Red tail vs Thorur: 1d20 + 8 - 2 ⇒ (11) + 8 - 2 = 17
Damage: 1d6 + 2 ⇒ (2) + 2 = 4
Blue tail vs Bahram: 1d20 + 8 ⇒ (12) + 8 = 20
Damage: 1d6 + 2 ⇒ (3) + 2 = 5
As Thorur marches toward Khāṇa, he also marches through the barbed tails of his foes, and they leave their marks upon him. His magic does its work, however, and Khāṇa finds many of her wounds closing in seconds. His work does not go unpunished however, as the amphiptere struck by his spiritual weapon retaliates with its tail against his exposed back. Thorur takes 16 damage from 2 AoOs and a tail strike, Khāṇa heals 9 HP.
The other one cautiously advances on Bahram, striking him again with its tail even as it dodges out of the way of his arrow. Bahram takes 5 damage.
Round 3
Gillie -4 HP
Yates -8 HP
Eòshli
Green Amphiptere -15 HP, AC hexed for 6 rounds
Khāṇa -5 HP
Bahram -13 HP
Thorur -16 HP
Red Amphiptere -2 to attack for 5 rounds
Blue Amphiptere
Bolded characters are up!

GM Losonti |

Blue fails its save, so it is hexed for the next 7 rounds.