Experimental gunsmith is really flavorful and I would like to use but it seems like a rather weak archetype with the loss of gun training.
The innovations seems pretty weak, with the exception of expanded capacity. Expanded capacity seems to be the only way that the gunslinger can make up for the loss of dex to damage. To maximize the damage gained through this it makes sense to give something with large base damage, any two handed firearm really, an extra barrel.
However, the experimental gunsmith can not be used with musket master and as such it will require a move action to reload if you don't want to deal with the massive misfire chances of alchemical cartridges.
What do you think a good way to get around this issue? Use a double barrel double hackbut/culverin or a triple barrel musket and hope you kill the enemy in the first salvo or spend the next two turns reloading?
I'm thinking the Experimental Gunsmith is best used as a debuffer. The extra barrel is, I agree, the best to pick. My next best pick is the alchemical vial launcher. It will allow you to start the round with a nice debuff that scales in DC to your Wisdom and level/2. Chuck a tanglefoot bag and start hitting an entangled touch AC.
You'll need to take the Gunsmithing feat properly if you want to start making other experimental firearms. (Although I must say I like the sound of a Culverin with two barrels.) This is something of a good idea in that the advantages of one innovation often contradict one of the others. That and Dragon Pistol would be a good thing to use as your primary weapon. The basic pistol is probably what you'd take otherwise since it's the only thing you could expect to get a full attack with early on.
Expanded Chamber is sad when compared to the normal Gun Training ability. I'd say it's the least viable.
I'm curious as to what you could accomplish with the grappling hook. It's got a particularly nasty drawback. It could make for some very cinematic moments. It would also encourage you to make grapple guns for the rest of your party so you can go out and hunt dragons by shooting them with grappling hooks. I can't be entirely sure that they don't mean grappling as the combat maneuver. Grapple at range?