OK. Still getting nowhere on this problem. The plug that my son thought was charred merely had some greasy fingerprints on it. And yes, the new connector was soldered in place.
Here'* where I'm at now. I have tried the 4th new CKP sensor, including one by Standard Ignition and AC Delco. Still the same results. I ran it today for 5 minutes and was fine. 5 more minutes and no restart. I checked for power and ground to the sensor and had identical readings both when it would start and when it wouldn't. However, no signal from either the 3x or 18x side.
Now I went a step further. I took the old connector (that is likely fine) and tried to get a signal with it out of the car. I supplied it with 12v and a ground directly from the battery. I can't get it to produce a signal this way either.
My new question: Can something go wrong with the sensor rings on the harmonic balancer? They do not seem to be out of round and aren't contacting the sensor. Any other ideas? I'm really stumped. Please help!!!!!