New isn't necessarily better.I think I’ll replace the whole electronic ignition package to start. Pretty cheap kit and would hopefully eliminate most of the things it could be.
If that's an older conversion, with a Chrysler built distributor, replacing it with the offshore version is a big step down.... and that's all you can buy new these days. Pretty much the only thing that would go wrong in the distributor is the pickup.
Now, if you want to throw parts at it, an ECU (the box) is a good place to start. I usually don't like to see parts replaced to diagnose, but the ECU is a really good spare to carry if that turns out not to be the issue. There are some diagnostics you can do on the pickup, but again, intermittent problems can be tough and that's another spare to carry.