Please define exactly "what you mean" by "HEI." Is this some aftermarket dist that looks like a GM original in-cap HEI? Or do you have some distributor hooked to an HEI module?
Do you still have a system with a coil wire? What does the spark look like there?
Measure power to the ignition system WHILE CRANKING and then measure battery voltage WHEN CRANKING and post them back
Until you talked about swapping things out, I was starting to think "problem with the distributor pickup/ reluctor" but if you changed the entire distributor..................then no