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I feel that what's already been said quite covers most of my points effectively, but I must reiterate a few.
The first is that Grit really ought to include some component wherein a character's natural talent is considered. Whether it's a pool that's 1/2 Character Level (minimum 1) + Wisdom Modifier like the Magus's Arcane Pool and the Monk's Ki Pool or 2 + (Level * 2) + Wisdom Modifier like a Barbarian's Rage and Bard's Perform. Even spell casters enjoy extra spells from higher ability scores. That said, given that there is a refresh mechanic, I think that the Magus's pool size would be most appropriate. Furthermore, this is your class, so while this is my opinion, I can respect why you wouldn't choose to follow it.
The second of the points is regarding the range of the firearms. While they're in the right ballpark for me, I find some of them too long and some far too short. If I were to suggest a range correction, I would suggest using the ranges listed in the firearms section of the Pathfinder Campaign Setting book. If you did, the pistol and revolver would have a range increment of 60 feet, the musket would have a low but tolerable 90 feet, the rifle would have a gorgeous 150 feet, and the scattergun would have a range of 30 feet (which makes sense because, really, shotguns don't have that much spray; they're not blunderbusses).
The third is my own point, and one without much importance. So far all of the guns have had a crap tier version of themselves in your gunslinger writeup save for the scattergun. I think it would make sense to include a blunderbuss which would have, according to the writeup in PCS, a base damage of 2d6 and a range 2/3 of the scattergun's range, same as a short-scattergun. This, though, is really just a matter of choices. I would like to see a terrible, single-shot version of it, but it's far from essential.
The fourth is, again, a point of my own. If you want to have people cry foul regarding the historical accuracy of a spring-fed bolt action clip for the rifle, you could tweak the fluff slightly so that it could either be a spring-fed clip or a revolving action. It could be phrased, for example, like this: "and the ability to accept multiple rounds through a spring-loaded clip or revolving cylinder." I only suggest this because I foresee a spring-fed clip being a point that people will whine about well after mechanical problems are actually fixed. If it helps your decision at all, the Colt revolving rifle predates spring-fed clips by quite a few decades. This way you can have rifles with multiple-shot actions without having to worry too much.
These are things that, in my opinion, demand not correction, because there is nothing wrong with them as they are, but certainly some polishing. I can appreciate reasons why, with each of them, you might not choose to make corrections. I only hope that you'll consider them when making your next wave of corrections to this awesome class.