handloading will get you "anything" you want, of course, but subject was (as others noted) factory loads
also as noted, pretty much any factory handgun round gains speed out of a carbine vs. a revolver (maybe not target wadcutters or CAS/SASS loads, but I don't think that really has much to do with OP)
not sure why OP is looking for milder out of a 357 carbine (357 is really mild felt recoil out of lever actions), but he is
instead of looking for "special lite" factory made 357 cartridges, gosh, that's pretty much what 38+P is, and no shortage at all of 38+P factory rounds easy found
the chamber cleaning thing ???
way, way overhyped, be it handgun or carbine, with merely modest attention to practical common sense cleaning of gun
it's not a bottleneck cartridge
and Marlin 1894s and/or brazilian '92s can handle a whopping lot more stress than 357s will put on 'em
maybe overthinking the "problem" ??
especially, as was noted, if kept only as HD gun, suggesting that if full house 357s unwelcome, no big need to worry about whether chamber 'ring" fouling matters a whole lot or not, just load 38+P and be happy, no ??
not meaning any that in contentious mode, but has anybody ever heard of a safety or gun malfunction issues from running a steady diet of 38+P ONLY thru a 357 carbine (or 38sp ONLY thru a 357 carbine, for that matter) ?