So in short, what I see from this analysis, debuff buckshot (from 22x8 to 20x10 perhaps), and buff mil and heavy shotguns (perhaps by bumping their Snap range to 8, so the slugs work better - the hv. shotgun fires 28x3 slugs which is already equivalent to a rifle's autoshot). Combat shotty is too weak with 20x5, maybe up to 22x5. CAWS might use a slight range increase too.
That could work, personally, I think that giving Shotguns armor damage would be a quick way to make them the end-all-be-all weapon of choice, I think that the DB and SDB are fine as they are, a long-term solution would be to give them different ammunition available, maybe acid rounds or an upgrade to them so you could produce a laser version of them (imagine how awesome it would be to have a sawed-off laser shotgun, makes me drool thinking about it), much like what you have done with the Tommy Gun. The Combat Shotgun is good, but could probably use a small buff, your suggestion of 20x5 > 22x5 would probably be enough to see them used more often. Again, seeing some different ammunition for the Combat Shotgun would increase its longevity, and give more reason to pay its costly price tag. The Domestic and Heavy Shotguns I don't have too much experience with, I find the Heavy SG to be good with what little experience I have with it, but it could maybe benefit from higher range and/or accuracy. The Domestic Shotgun I have never used, its damage just seems too low. Maybe a buff from 18 DPP (Damage Per Pellet) to 20 DPP would help it out, but it is also unique by being able to chamber stun rounds, a little indecisive on that one. Hopefully these suggestions help out, I can mess with the ruleset and see what these changes would od if you would like, but I think this would make Shotguns in general better, without being OP.