OK, crossing my fingers, but I think I got it working right.
I re-did all the grounds and all of the connections, except for the ones inside the headlight casing, and checked, no change.
Moved to the rectifier. Stock-type rectifier--this thing gets pretty hot, I can see why people swap these out for modern ones. What was odd was that it was not attached using the connectors shown in the shop manual, but soldered to the other wires (pretty shoddy job, too). So it's definitely been messed with. The grime on the connections tells me it wasn't too recent, though. Did the ohmmeter tests recommended by the shop manual, and they indicated that the rectifier was fine. So I rigged up bullet connectors to connect it back to the electrical system. Fired up the bike and everything was magically working more like I'd expect. 12.5 v at idle, about 14 at 4,000 rpm. I only have an analog multimeter, so that's not exact, but definitely better than maxing out around 12.5. It was dark by the time I finished, and I'm not used to riding yet, so I didn't ride it around to see if it would die yet. But I'm thinking it might be fixed. Must have just been those connections.
Thanks for all the help, everyone. You guys rock.