Man, I did the same. When I had your problem, bought a new system with distributor, ECU, ballast kit. It did not solve it. Had to go back to basics. When it starts in the "start" position of the ignition switch, that is the primary system. This bypasses the ballast resistor. When you go to the "run" position or let go of the key, it is in the secondary system which goes through the ballast resistor. Once I figured that out, I had to check my wires to ballast. Mine is the 2 prong ballast. When I pulled on one of the wires, it completely came out of the terminal. That was my "aha" moment. Maybe the wire in yours were tight, but how much copper was actually crimped in the metal terminal? Was this part of the new harness you got?
When I got my car, it was running like a gem. 3 yrs later, i started to get your exact problem. I to was getting frustrated as to what happened from the last season of working great to the intermittent problem, then it was dying all the time after I release the key to "run." So it sounds to me it is your seconday circuit that is having problems.