It's back!
Well, today I picked my bike up from the shop. It was back in running condition and was working fine! I nearly froze to death on the way home.
Turns out that the guy at the bike shop didn’t really have much more clue what had gone wrong with it than I did. He couldn’t get the bike to start, so he start poking around in the electricals surrounding the starter. He couldn’t see anything wrong, so he took it all apart to have a closer look. Still not finding anything wrong (and, naturally, the bike’s computer didn’t have anything interesting to say either), he put it back together—and the bike started! His theory was that I shook a connection loose somewhere along the way.
The total cost of the fix to me, including labor and the tow in the first place, worked out to the grand sum of—absolutely free! I do like my bike shop. (Connecting Rod in Eifukucho, just to ensure they get a plug.)