Well, good news, bad news. New CDI boxes are in, but when I installed and tested the first one, it only fired on one side. I tested the stator voltage and trigger voltages again, and found that the trigger voltage was cutting in and out intermittently. When I tested the trigger voltages before, I forgot to cycle the spark advance back and forth while testing.
Problem endured even when I replaced some of the spade plugs, just in case the connection inside that black heat shrink had gone bad.
I think I'm going to need to replace the trigger, too.