The parts for the Uberti fit the 2nd gen Colts, and the cylinders will fit the 3rd gen as well. Both Kirst and R&D (Taylors) made for the Uberti will fit the 2nd gen Colt.
The bore at .375 needs either a heel based or a Hollowbase bullet. The Hollowbase is much easier to reload, as the heel type need a special crimp die. The R&D offers two cylinders, one through-bored for the 375 barrel, and another option with a stepped, throated chamber (like a standard 38) for a relined barrel in 357. I don't know if Kirst has the two styles of cylinder or not, as my Kirsts (and R&Ds) are made to shoot through the original .375 bore, and I load 148 gr. Hollowbase Wadcutters in 38 Special.
I've never had a problem with either brand of cylinder or any accuracy problems with the HBWC bullets. I found the best bullets to be the Remington brand bullet (hard to find) which has a messy black lube that works very well, but requires cleaning the seating die much more often. Next is the Speer, which, with smokeless, will lead a bit. Last is the Hornady, which leads more because of its knurled body, which presents all those points to the bore to rub off lead without rings to scrape with. (I presume).
Both Kirst and R&D have cylinders that are "drop-in", but require the barrel to be removed to load/reload. Both also offer versions with gated backplates for SAA style reloading, and require you to cut a loading port in the frame's recoil shield.