I don't disagree with the idea.

The "gun" rotation has so little presence in the kit today that you could make it work like BLM Fire.
Get a stance mechanic during which you use the multitool as the gun. Replacing your base GCDs with stronger ones and Ricochet/GR with stronger versions or keep them. Fail to maintain the stance and you got back to your little shooty. Hypercharge could fill this role.
Problem with that solution is you won't see your main weapon anymore or rarely.

A Gunslinger/Musketeer job also needs to be unique in its own. It could also use guns as RDM, PLD, DRK uses swords (Can also extend it to SAM) or BLM/WHM uses scepters.
Ammos, however, were annoying and ininteresting. In my opinion, it should work like SCH, ammos being required for unique abilities or adding extra effects on those abilities. However is should be either defensive, either offensive, can't have a mix of both.
I'd also love to see a "Mustadio-like" mechanic with aiming. Instead of using regular combos, Gunner would use "Flank Shot", "Leg Shot" to find the target weakspot and prepare a "Headshot" GCD.

Or as a Gunslinder, it could rotate between multiple weapons. Guns don't come in one forms, you could have a gunslinger stance blasting with two guns, a stance using bigger guns to deal colateral damage to other targets, sniper stance, and so on.

Nobody said we couldn't have two jobs using guns as we have many sword users that plays differently.