Good news- I found a problem!

Tonight I checked the points and the timing, as per the service manual. The points gap is right on, right at spec (0.014-0.015 for both), so I went on to adjust the timing... but I just couldn't get the left point to test as open. Even when I could see the gap between the points, nothing I could do would make my multimeter stop beeping, except for turning the engine a bit farther... but I couldn't see how that was changing anything--

...until I realized that the continuity broke when the right point opened! I disconnected the points from the rest of the electrical system, and sure enough, somewhere north of the points, the left and right wires are shorted together. So every time either one of them closes, both plugs fire.

My guess is that I didn't notice this issue because I was only running on one cylinder- so the plug firing too often wasn't so much of an issue. But now that I have it running properly, that accounts for the backfiring and the misfiring and the rough idle, right? (Please say yes.)

So tomorrow I'll dive back in and start tearing the electrical system apart. It needed a lot of work anyway... might as well get a problem fixed along with it.

As a plus, doing the points and the timing was nowhere near as daunting a task as I had imagined. And, I drained the oil and realized that it was half-gas from all the overflow that was happening before I had fixed the floats- better get that fixed too.

I'm well on the way to riding again!

Excellent!