FINALLY! Found the reason for the ever-stoopping engine. Went to a friend of mine who's Mexican but also a US Citizen and owns a custom VW shop. I asked him to look at the problem or recommend someone he trusted. He checked it but first attaching a pressure gauge to the fuel line (37-40 psi constant). It wouldn't stop while I drove it so he drove it and it DID stop on him.
We got back to his shop and he said "not a fuel pressure problem so it's gotta be an energy problem." I left the car with him for a couple hours and he called and said that what I'd normally call the "coil" which is a black box affixed to the driver's side of the engine and has 4 plug wires coming out to the plugs (no not a distributor). Anyway, he said when he removed it, he noticed that two of the steel power rods that deliver spark to the wires were cracked. He heated the unit up and found that, at engine operating temp, the cracks separated. Ergo, no spark to cyls 1 and 3.
This is a real hidden problem with this little car and hopefully, someone will benefit from the weeks of hair pulling over this one.
THanks for all the assists. It was appreciated and eye-opening.