Cranks but won't start. Unplug ground at field spade on Alternator and it starts?

I don't know anything about unilites but I would be tempted to swap it out just to change the problem. Either just slap a breaker points dist in there, or find a Mopar stock breakerless dist and look up the HEI module conversion. It is not very hard.
The rotor for my Unilite 47 series distributor, MAL-322, is discontinued. Was hoping to put a Pertronix conversion kit, they have one specifically for Unilites, but without a rotor that distributor is now a paper weight.

Local parts store say they can have this single point unit in today. So I can throw that in and put a Pertronix kit into it later or just keep it around as a spare.

Distributor Single Point.jpg