Since I wrote last:
Replaced the whole distributor last week. Running great until...
...wouldn't start last night. Again it was a rainy day.
Waited ~3 hours and then got it to start (BARELY!).
Someone suggested the voltage regulator. I didn't think it would have anything to do with starting, but for $15, I'm willing to give it a try.
I am also thinking about replacing the ignition switch.
Grasping at straws.