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We have a large party of seven 6th level characters, created with a 20 Point Buy. Every one of them has considerably better attack and damage bonuses (and AC) than the pre-gens that come with the adventure (and the adventure was designed for 8th level characters).
Based on my calculations and running them through encounters, it looks like I have an EL 9 group. (Meaning, roughly, that the party functions like 4 9th level characters.)
Does this sound accurate?
Party composition:
1. Ranged Fighter (composite longbow with rapid shot / multi-shot)
2. Melee Fighter (specializing in two-handed greataxe with power attack and great cleave)
3. Paladin (tooled out for smite evil)
4. First Cleric (tooled out for maximum effectiveness of channeling)
5. Second Cleric (focusing on buffs and second healing)
6. Sorcerer (specializing in damage: magic missile, scorching ray, and fireball)
7. Rogue (specializing in bluff/feinting)
Without knowing where they are on the Wealth by level table(and the melee character's primary magic equipment), I would put them at Least EL 8. You have a lot of front line bruisers, but not too much by way of spellcasters. I would be careful if you are stating out high EL encounters that can fly, as it looks like you only have 1 fighter and the Sorcerer who are well prepared for this (from what you've given us, at least).
First, a word of warning, be careful with that math. Just because the party has the damage to take on a EL10+ encounter doesn't mean they can soak the damage from those encounters. We had a big problem with this when we were running a 6 man group. When the DM sent single monsters that were strong enough to threaten the party, those same monsters were capable of killing both of our front line fights in a single full attack. Don't use single monsters, try to use multiple weaker monsters and spread the damage around.
A humanoid with 6 levels of player classes in EL 5. 6 Humanoids is CR +5, so that puts the party at EL 10. Elite stat array is +1, you stat buy is better then an elite array, so make is +2. Then the players should have much better gear than most NPC, so add in another +1. That puts your party at around EL13.
Fighting an encounter equal to your own groups EL is fairly epic and the group generally has about a 50/50 chance to win. So if EL13 would be an epic encounter for the group, that puts the average player level(APL) around 10. A pair of CR8 monsters should be an average encounter for that group.
Assuming that wealth is average by level I'd say high EL 7-8. Against melee brutes your PCs are going to romp (unless the AC of a monster is incredibly high) but like kirstov said you are going to struggle against mobile artillery and controllers until you have reliable ways of dealing with ranged flyers and casters.
Even the absence of a reliable source of haste and flight can make many encounters significantly more problematic than they might be with a second arcane caster.
Additional mooks supporting the encounter might be a better solution than either doubling the number of big creatures or buffing the big monster into the appropriate EL.
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I have a similar problem with my group of 9 5th lvl characters in my game. The best solution I have found is to make nearly all significant encounters a mixed type of encounter. By that I mean, have some swarms, some same level CR mooks, a big bruiser, and a buffer or caster type. I started adding in an occasional enemy with bard levels or a channeling cleric type, and it has made a big difference in combat challenges being more balanced. The swarms especially are nice because they are sort of a nuisance and can be cleaned out in a round or two of low level spells, abilities, etc., but being sickened is a nasty effect and they do eat up some party actions.
First and foremost be careful of two things... a single high level BBEG (or even two) is going to do one of two things...TPK the party or get stomped quicker than you think. Or even worse, inflict damage on the party that they cannot repair (petrified, etc) with their highest level spells, even though the encounter level was mathematically sound.
I also used the method Monte Cook suggested in his articles on running larger parties, where you start weak and throw increasing levels of challenges at your party, until you find the right level of difficulty for your group. One thing to factor in is that no calculation of EL is going to take into consideration the uber teamwork, crafty thinking, or super efficiency some of your party may display.
EDIT- One last piece of advice, get yourself a copy of Herolab with the Bestiary data sets, it is worth its weight in gold to GMs running larger parties. You can quickly add a few class levels onto a monster of any sort and get an accurate statblock, which is extremely useful in this sort of situation. Nearly all of my non-speedbump type encounters for the party are regular creatures with a few levels of a class tacked on, which as an added bonus keeps the party guessing and on their toes. Nothing makes a melee class want to bash a typical bruiser type monster like adding a few caster levels to them! :)
More than 4 players makes the CR system cry. :)
It really does strain it. Each additional character is not a % addon (in other words, increasing from 4 to 5 is not a 25% bump, it's more like a 35% bump) because you have more resources to spread around on the encounter.
What I generally do is assume each additional character boosts the EL of the party by +1. With 7, you've got a +3 right there (making them the equivelant of a 9th level group). It sounds like you're also boosting their equipment and stats, so that makes it even more unbalanced.
In my experience, what you've done is basically toss the CR system out the window at this point.
As other's have pointed out, the easiest way to handle this is to send multiples up against them. To get a level appropriate encounter, I'd use the following :
8 6th level enemies with MW equipment, and a single 8th level leader with +1 equipment.
OR
1 8th level leader (+1), 4 6th level enemies with MW equipment, and 10 3rd level mooks with basic equipment.
OR
1 10th level leader (+2s), 2 7th level lackies (+1's), and 10 3rd level mooks (regular equipment).
Basically, you'll want to hit them about 2 to 1 with lower level grunts, on average.
Here Are my calculations
party of seven 6th level characters with average stats (20 point buy) and above average wealth, alognside mediocre skill in optimization and tactics. i would say that EL 8 would be fine. thier gear compensates for thier mediocre tactics and optimization and 20 points is PFS standard. but 25 point buy doesn't really affect APL either. their only real advantage is numbers.