SASS has a category just for you: Frontiersman; requires BP or a sub in all 3 firearms. Handguns can be any cap & ball revolver of .36 caliber or larger (less than .50, btw), 5 or 6 shots. 5-shooters must have the hammer rested on a pin between chambers. Unlike cartridge guns, there is no minimum power factor or fps... Additionally, cap & ball revolvers are legal in EVERY SASS category, so while my comments are directed toward Frontiersman, you can enter another category & shoot that heathen smokeless in your rifle & shotgun. A couple of the categories have restrictions on bore size and model rifle or shotgun, but that's a wholly different topic.
I'll answer your Shotgun question first. Just about any firearm has an equal opportunity to come off the assembly line on Monday and Friday. You pays your money & takes your chances. However, that said, I have a pair of IGA Stoegers I bought back in 1985 when I started shooting CAS matches. The only thing I've done to either was to disconnect the "auto" safety feature. Safety still works, just doesn't engage every time you open the gun. I prefer double trigger guns, and while most are set up with the front trigger being the right bbl, a lot of folks swap the triggers as they can engage the second (rear) trigger faster. I've left mine alone. Most speed freaks in this game use a single trigger gun, the SKB 100 & 200s being the most popular, with the Browning BSS a close second. The most work will be simply smoothing up the action, polishing the chambers to aid extraction, & smoothing, lightly removing square edges off extractors. "Funnelling" the chamber mouth is touted as being the cat's meow for loading ease, but, IMO takes years off the life of the gun. I've seen relatively new guns ruined by this butchery. The shotgun is where you win or lose a match, but... practice is far more beneficial than any so-called "trick" 'smithing.
I have used a ASM 1851 since 1986 when only one sixgun was required. It has been modified with a Manhattan conversion, & a Ruger handspring & plunger. I now have 5 Colt 2nd & 3rd Gen 1851, 3 of which have the same modifications as the ASM. I do have 2 spare cylinders, but... they're in reserve, not utilized for matches, just in my spare parts inventory. My guns also have "Heinie" trigger/bolt springs ala, a Colt Peacemaker (SAA). Mostly a drop in part but might need the trigger leg shortened a bit. I now use SlixShot nipples exclusively, (I've used Tresos and factory nipples, and find the SlixShots the best of all). I typically load the two guns I'm going to shoot for the day at home (powder, lube wad & ball only), and then can simply cap at the loading table, using the same cap one, skip one, cap four that one would use with any Colt type action, this sets the pistol up that after capping that 4th in row, pull to full cock and ease the hammer down on the uncapped nipple. I do charge all six chambers, but only cap the five. I've never had a chain fire, but one could happen, I suppose, any time. After shooting my stage, and clearing my guns, I set up on the unloading table (a position to ensure everyone's guns are fully emptied at the end of the stage), and charge my guns for the next stage. I try to ensure I shoot early enough in the rotation to accomplish this. It usually takes me between 3 & 4 shooters to charge my guns. Instead of a "Manhattan" conversion one can go with a "cap rake" to keep spent caps out of the action. An "Action guard" is a new to me thing, and I can see the benefit of having one installed, tho' I haven't yet. I load my .36s with 15 grains of Goex, (probably a little less as I load from a flask with my thumb over the spout and this makes a depression in the powder the spout holds), a lubed wad (usually from Cabela's, available on-line), and a .375 round ball. I don't bother with lube over the ball, makes a mess for questionable benefit. I don't know how using a sub could affect my reliability as I haven't used them as yet... (rather since I quit back in 1987 using "rust in a can," aka: Pyrodex). I can shoot all six stages at our monthly matches without disassembling the gun, or even really wiping 'em down. (Actually, I've fired several 3-day matches without cleaning or more than a cursory wipe down between day one and the end of the match). I doubt the most strident Pyrodex supporter would attempt that)! I use a Ted Cash snail capper, usually holds enough caps for a couple of monthly matches... may need topping off if not completely full to start. I prefer Remington #10s, but have used RWS 1075s & CCI #11s. Remington #10 have a longer skirt and hold better (IMO), but often need "seating" to be fully seated. I either use a bit of flattened antler as a "seater" or simply flip the capper around in my hand to use the backside of the capper to get the cap fully seated on the nipple. Failure to do so sometimes results in needing a second pull of the hammer to fire the cap, and that takes unneeded time. In my 30s, 40s and even into my 50s I was a fairly good competitor, winning several matches in my category... now in my 70s, I'm not so inclined and often find myself just loafing along, working on "clean" stages and matches. Frontiersman category requires one handed shooting, which I neither enjoy, nor practice at. So I'm slow... get over it, or practice... the 8th deadly sin IMO! LOL!
Lastly, the rifle: Fast shooters prefer the 1873. And to be fast it needs a short stroke kit. They can be installed by a competent mechanically inclined do-it-yourselfer. For the Uberti version, you'll also want to replace the lifter, lever & trigger block springs. I use SlixSprings in both my 1873s & 1860. Fast shooters prefer 38/357 chambering, but you'll probably need to anneal your brass to keep the action from fouling out, same with 45 Colt (all 3 of my toggle-links are 45s)... although I've trimmed my carrier block to be really loose, (taking about .005" off each side) and can run my rifle for that same 3-day match without bothering to tear it down to clean... Tho' in all honesty, I have noticed a slowing of it towards the end of that 3rd day! The .44-40 can be a bear to load if you're not paying attention to details, but is by far the cleaner option, as would .38-40. But... as with the .44-40 & 45 Colt, reducing BP loads is a bit more problematic (I don't care for fillers). I have my 1860 converted to fire the Cowboy45Special (a 45ACP length case with a 45 Colt rim) and can shoot as light as a 160 bullet with reduced powder charge with impunity. However, because it's a straight walled case, fouling is a problem. Because of the modifications to the carrier, I don't feel as confident thinning it down as I do with the factory carrier. I've just acquired an annealing machine and will experimenting with that in the next few months.
Here's a new book by an icon in the game:
George Balyor's "Big Bad Book on Cowboy Action Shooting". I haven't read it yet, but if his articles in the SASS Chronicle are anything to go by, it'll be worth the investment.