What are you trying to accomplish with this build?
The problem is, without some sort of action economy boost, it is likely that you can't buff and then fire the next round for as great of an effect as you would get from just shooting both rounds. Your archer would be a better archer if he didn't have levels of sorcerer. And of course, levels of archer weaken the ability to be a good sorcerer.
I just don't see a lot of synergy between the two classes, both using wisdom isn't enough.
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Honestly, I don't think you need more than one level or two at most of Empyreal Sorcerer if your main aim is to be an archer, you get a bunch of Gravity Bow and maybe Shield spells which add quite a bit to your build and you don't push back the Zen goodness too much. Mashing them together will possibly give you more options, but you're going to give up a lot of potential to do so, far too much in my opinion.
For the action economy problem, I say you could solve that by tanking the first round (swift action for +4 to AC and relying on Snake Fang) while you cast gravity bow. Drawing attacks and forcing enemies to miss (waste their attacks) is good action economy if it works.
Snake Style is workable whether you cast gravity bow, or shoot a bunch of arrows. If the first round is a surprise round that you act on, this is probably an ok strategy, but in regular melee combat, it will probably take quite a few rounds before your bonus damage from gravity bow equals what you could have just gotten by the shooting that first round, and sooner damage is better than later damage, since it reduced the number of times the bad guy hits you. If in the first round of combat your party could have brought down one of the bad guys if you had attacked instead of buffing, you probably should have been shooting.
And then there is the fact that your monk 4/ sorcerer 6 is spending a standard action to increase bow damage to 2d6, a monk 10 could spend a swift to get 1d10 (2d6 at level 12).
I think the concept is interesting, I just don't see the math working out.
It comes down on what you're wanting from your character. This character can be built and played very differently depending on what you're wanting.
Monk X/Sorcerer 1, lets you use wands and a few spells, probably don't need magical lineage.
Monk 1/Sorcerer X, Lets you get an AC and Saving throw boost to your spell caster, and lets you use a bow as backup.
Going more of one or the other is really determined by what you're wanting this character to do. And the optimal choices are different depending on which.
Note that you can't take Eldritch Knight without a level of a class that grants general martial weapon proficiency.
Arcane Archer doesn't have that issue, but it has pretty brutal entry requirements and fewer spell levels once in.
One level of Zen Archer, one level of something that qualifies you for Eldritch Knight, and then six levels of Sorcerer will qualify you for Eldritch Knight with as much spellcasting intact as possible, but you'll have to go dex-based and won't be able to grab Point Blank Master until very late. If you don't care about the save DC of your spells then that shouldn't be that big a deal, though you'll need to figure out what to do about close-combat situations. You'll end up with 3 non-casting levels, which still grants a fair deal of spells.
If you're trying to stack wisdom to be a full-blown high-save-DC Sorcerer along with using Zen Archery and a full-BAB prestige class, you'll end up with at least 5 non-casting levels, meaning your spells-per-day will be lousy anyhow.
Either way, multiclassed Zen Archer suffers from getting neither Rapid Shot and Manyshot *or* additional flurry attacks.
If you really want a powerful arcane bowman, I'd consider a Strength Patron Witch crossed with Eldritch Knight to get Divine Favor with more standard archery. Inspired Blade Swashbuckler/ Witch/ Eldritch Knight can be a pretty mean archer/swordsman and also eventually throw Quickened Ill Omen or cast Divine Power.
well you get an extra attack at lv8 of monk.
You're losing out on an extra bow attack at level 8 Zen Archer.
You're losing out on an extra bow attack at level 8 Zen Archer.See above
At 8th level, the monk can make two additional attacks when he uses flurry of blows...
The Monk gains full-BAB iterative attacks when using flurry, so flurry gains the +6BAB iterative at level 6, and then a second bonus flurry attack at level 8.
At 8th level, the monk can make two additional attacks when he uses flurry of blows, as if using Improved Two-Weapon Fighting (even if the monk does not meet the prerequisites for the feat).
But your response has me curious. Were you planning on being an Unchained Monk?
They don't, but your comment of getting another flurry attack is true for the unchained monk. So I was checking if you were trying a zen Umonk, so I could tell you you couldn't do that.
So now we factor in something. You're waiting till lv9 to get your lv1 spells.
So casting gravity bow that lasts for just a short time is instead of having a full attack of 4 arrows, 5 if you spent ki. Just for the increase of 2d6 from 1d8, which means you need like 4 rounds or more to make it worth it (didn't actually do math).
Also now going to monk 9 gives you more AC from your barkskin.
It's not a bad choice to go into the Arcane Archer this way, just that you're not actually going to be gaining much from it.
The kind where there's no surprise round? Otherwise battle has already started. Could I spend a round to cast gravity bow? Yes, but like my fake math shows, you'd need a 5 round combat to come out equal to having just attacked the first round. And since combat usually lasts 3-4 rounds you're coming out behind from casting r1 instead of attacking.
It does sometime rarely, but not the default, nor common.
The kind where there's no surprise round? Otherwise battle has already started. Could I spend a round to cast gravity bow? Yes, but like my fake math shows, you'd need a 5 round combat to come out equal to having just attacked the first round. And since combat usually lasts 3-4 rounds you're coming out behind from casting r1 instead of attacking.You never have battles where you control when the combat begins?
For instance, you never have instances where there is a door closed and you have to enter it before battle really begins.
Sometimes that happens. Those are usually the easy battles. It is being good at the hard battles where things matter.
Spellcasting isn't specifically mentioned in the Perception Skill, but verbal components are described as a strong voice. Hearing the details of a conversation is DC 0, 5 through a door, just hearing that words are being spoken is probably somewhere between the details of a conversation and a battle, so call it -5, 0 through a door, perhaps a few more for distance, so if you are casting spells before opening a door you have almost certainly blown your chance at a surprise round and possibly given them a chance to prepare just as much. Or burst through the door themselves surprising your party.
You never have battles where you control when the combat begins?
For instance, you never have instances where there is a door closed and you have to enter it before battle really begins.
Different people play this very differently. Some people play it very mechanically, where characters just sort of drop onto a battlefield on round 1, and that's that; other people play it where you're essentially always getting surprised (even if there isn't technically a surprise round involved). Things like casting a buff while moving into an area (where you wouldn't get a full attack anyways), or casting a buff because you know something is approaching, or casting a buff because you know you're approaching something... these just don't factor into that style of play.
Well for your thing to work well you need doors, and you need to know the enemy is behind the door. So you have to be able to take your time to figure out that enemies are behind the door.
Opposed to, exploring the sewers or a cave where there are no doors, out in a plain with no walls or doors, in a forest, underwater, getting ambushed, enemies that know you are there, having players wait long enough for us to find out there's something behind the door rather than just opening the door and finding out that way, remembering to tell them to wait cause you want to buff before opening the door.
So for me, having a short 1-3 minute duration buff will very rarely be up before combat.