Mystery solved. It was the module. Even though it sparked, it was either off timing or it was not strong enough.
I had noticed that it wouldn't jump the wide gap of my tester, but it gave a strong blue spark over .030. I have a spare 301 in the barn but it's cold here and I didn't want to pull the coil off and the shroud bolts aren't lubed, so I ended breaking one off.
Anyway, I braved the cold, put the new mod on, it jumped the tester gap, and started right up. Merry Christmas to me and to those who helped with this thread.
For reference, here's a case where a mod fires but won't start the engine.
Thanks all.