Runs, drives, dies

If the dist has mileage on it AND the vac adv is connected, the constant flexing of the p/up wires can cause them to break. Seems odd though that this normally random occurrence only occurs hot & not at other times. To check, disconnect dist plug & connect an ohm meter to the p/up. Wiggle the wires. Resistance should be 150-400 ohms & not change. If it goes open cct, bad p/up. Pretty rare, have never seen it personally, but p/up may be grounding internally when it gets hot.
You need to find out what value [ ohms ] the ballast res needs to be for THAT coil. The Chrys bal res is 0.5 ohm. If that coil requires, say, 1 ohm, then the coil will be getting excessive current & will run hot. Coil could have an internal o'heat protection device that is tripping.
Also check that you are getting 12+ v to the ballast res & ECU with the engine running.