One thing I like for low-tech, alternate firearms (which works for alt-history, fantasy-with-guns, and of course AtE), if the local producers can get away with it, are black powder revolver rifles. I typically design them as 5-shot weapons, both as a mark of "This isn't the world you're used to" and for a somewhat-gamist reason -
Low Tech gives black powder firearms 5 shots before they need a fairly thorough cleaning or they start racking up Malf (and, later, Acc) penalties.
The sort of skirmishes you're going to have in AtE "warfare" may not call for a lot of shooting from each participant, such that 5 shots may be well sufficient (particularly if most of your opposition are using muzzleloaders). Additionally, you can use loose powder and shot, avoiding the need for cartridges, yet still have something of a repeating design. Granted, revolvers are best with percussion caps, which increases demands on ammunition manufacture (not quite as much as needing cartridges, but still an increase). Flintlock revolvers
are possible, however. A muzzleloader can handle higher pressures than a primitive breechloader or revolver, of course, so you may want to have your revolver-rifle using factions get less power out of their weapons than their muzzleloading enemies. Roughly speaking, and going off of the trend from 3e
Vehicles, a muzzleloader will weigh around half as much as an equivalent 5-shot revolver; equalizing weight by simply reducing power means the revolver would deal about half as much damage as an equal-weight muzzleloader. A better option is often to reduce caliber; 70% caliber will equalize weight and only reduce damage by 70%, although there's typically a reduction in pi-class to go along with it (so it'll do comparable wounding to the 50% power option, above, but have roughly 50% better armor penetration).
If your typical raiders are using something like LT's 0.59" caliver (3d+1 pi+), the ones with revolver rifles would be using a similar-weight 0.42" rifle that deals 2d+1 pi.
EDIT: Something I forgot - the length variable for
Vehicles firearm design is roughly the weapon's length in calibers, meaning, with it being held constant, the 0.42" rifle's barrel is roughly 70% the length of the caliver. That may be able to justify +1 to Bulk, making it a bit more wieldy, but I typically assume the big revolver cylinder would offset that, keeping Bulk as-is.
In case anyone's curious how I assume the weapon itself would work, I'm thinking the user would half-cock the hammer, releasing the cylinder to spin. He/she then manually spins the cylinder to the next shot, and pulls the hammer back to full-cock, which locks the cylinder back into place and primes the pan. That probably means a Ready between each shot, but either a Perk or a successful roll against Fast-Draw (Ammo) should be able to reduce that to a free action, if needed.