I think with how fun and unique the weapons all look, they also deserve to have distinct function and gamefeel, built into their base function, independent from their unique joker options:
Quad Cylinder
Unchanged standard fire. Firing while ADS shoots a 4-round burst, each cylinder firing almost simultaneously with a nice ratcheting sound. The delay between bursts is affected by fire rate%. Lower sustained damage than standard fire because of the delay, but better burst damage and accuracy.
(I just think it would feel nice, and fit the nature of how doohickey-y the gun is)
Shotgun:
Unchanged standard fire. Firing while ADS shoots a single shell. Holding down the trigger overloads additional shells into the chamber, one by one, affected by fire rate%. Releasing the trigger shoots all shells at once, a giant burst of pellets.
(Lets the shotgun fill both the role that it does currently, but also the fantasy of big hefty blast of buckshot, charging up before you dip in close to blet out a slab of damage)
Long Ranger
Standard fire ricochets among enemies - It deals damage to whatever it hits first, and if it kills, any overkill damage beams to the next closest enemy, then if that kills, it ricochets again, so on and so forth until the remaining damage fails to kill. Hitting a weakspot doesn't then headshot the next enemy or anything, but does increase the ricochet potential because of the increased damage "budget" from the first hit. Firing while ADS pierces, as it does already.
(Unscoped fire has less damage potential than a collateral shot, but can more easily clear fodder enemies without needing to aim or set up the same way)
Leveredge
ADS fire is unchanged, but standard fire is now a shotgun, with a very tight, fixed spread (perhaps 6 pellets in the shape of a little star, to be cute), effective out to long range.
(Lets the leveredge be both a lever action rifle and the kind of "sporting shotgun" archetype, without stepping on its own toes, i hope)