Yes, I called them. They asked me the questions about things I'd already checked. Yes, I'm giving it full 12v, the coil and the module. Weird. I'm going to change the plugs and wires just for the hell of it and see what that does.......and swap out the carb too. It just sounds very "ignition-ish" like a bad power connection, but it's not.
Someone told me (on another forum) that if you don't open up the spark plug gap to over .040, it will run like sh** with a Pertronix III. Now.....I really doubted that, but this guy on the other forum said he doubted it too, but sure enough, it worked for him. So that's something I might as well try.