1967 Barracuda 4 Speed 273 back fire issue

I'll venture a guess here and I'm certainly no expert but it sounds like to me you may have troubles in the ignition switch.

With all the damage to the ignition system, for example burned points, fried ballast resistor, hot coil, that would suggest to me that somehow the 12V the coil sees during "start" is not dropping back to the 8V it should have in "run"

Another clue it may be in the switch is you said you couldn't turn off the engine with the key and you had to yank the coil wire. I'd be looking at the ignition switch and possibly replacing it with a known good one.