Percolation? Heat soak? Don't drive during summer??

Before taking the car apart I could drive it anywhere in the city and did. Drove it on the freeway and down the strip on a hot September day and the only problem I had was due to overheating because I hadn't done the radiator yet...

Ah, I didn't realize it had headers still back when it ran everywhere.

Could be that when you had that buzzing coil issue something got cooked. I hate throwing parts at a problem, but in this case I might try a cheap parts store ecm (if it still dies, try @JPar's gas squirt first, and if that don't do it, swap your original ecm in. If it fires then, you'll have an answer). Then once you have a better idea, figure out how much you want to spend on igniton. A cheap ecm isn't trustworthy (two is one) but last I looked they were cheap.

If you really want to learn electronics, I might suggest an hei driver conversion as a project since getting good Mopar ecms these days seems difficult at best (but I'm no expert).