Gets hot and stalls out

Dana67Dart said
Bring some alligator clip extension leads.

Next time it happens try jumping around the ballast resister.

If that does not work try batt positive to the coil side of the ballast resister, or coil positive itself.

Basically what you will be doing is rulling out a bad ballast

And a bad ignition switch.

Will do. I don't get any backfiring, and it's starting fine when it's cool which is why I figured a heat-related issue, but know enough to know that this could be like chasing an electrical issue.