Very good post Lut.
Personally I think the chances of a 1877 frame being re- hardened would be slim at best and more probably non-existent. Some of the frames in the 165-180,000 range (circa. 1898) already in the system were factory smokeless hardened. They were BP frames in the system during the changeover to smokeless guaranteed guns (guaranteed #180,000 or later). The only chance this one had to be a smokeless frame is if it was returned to the factory, not a very high probability for a run of the mill commercial sales gun back then.
I agree with Jet also, but with this gun I would be a little extra cautious for two reasons, the .45 cylinder is the thinnest of all and by the time an "oops" shows up its too late to back up time and a $5000 antique is a boat anchor. A lot of posts in this forum ask how much they will save by re-loading...in this case, with one slip-up, it could very well end up being a "how expensive is it going to be to reload" nightmare.
BP with a "soft" cast boolit for me.