I too have had the exact, same hot start issues as the OP. I have '67 Dart, 273 V8, with the Mopar electronic ignition conversion.
I have not yet installed the electronic voltage regulator as suggested in the Direct Connection Racing Manual.
I'm not to the bottom of this with mine, all the voltage checks test good, at the time. Installed my spare coil and its been much better and not let me down lately.
When I had a no spark condition, I installed a spare control box, and would have spark, and fire back up. Next morning, plug the original control box back in, and it would fire right up.
I'm suspecting it may be a bad connection, maybe at the bulk head, or ignition switch, even though when it fails there is voltage at the coil and ballast resistor.
I'll post back when I am confident I actually have this issue fixed, but driving season in my area is almost over.
Stay tuned!