I rechecked the standing system drain per the manual, and my ohm meter read 0. The needle didn't even jump.
So, I pulled apart the regulator/rectifier, and found that pins 2 & 3 on the female connector were blue-green, and obviously oxidized from excessive heat. Putting a multi-meter on the R/R, I found that pins 2 and 3, when connected to the ground (pin 7) were providing significantly less resistance than the specified ranges.
Between the female pins being oxidized and the out of spec readings, I thought that I'd discovered the source of the problem.
I pulled the R/R unit, ordered a new one, measured the battery voltage at 12.6v, and then put the bike away for the night. In the two days it took for the new R/R to arrive (oh, sweet modernity!), the voltage on the battery didn't drop one bit. 12.6 on the meter when it came time to put the new R/R on.
After that, the bike started easily, but idled rough. Some fresh spark plugs later (all four were carbon fouled, and one of the exhaust pipes was cool from a non-firing cylinder), and the bike has come back to life.
The learning here is to just trust the manual, and run through the specified tests before wasting money on parts. Woops!