Hi Ted,
I had a similar if not identical problem some years ago. Turned out I had three separate issues, all with inter-related consequences.
1. Deteriorating fuel tank. If yours is the original you can be certain that fine rust particles will cause you an issue.
2. Compromised wiring to fuel feed pump. During the restoration, the restorer cut the wires to the fuel feed pump. When putting back together, he used wire crimp fittings. Great for a few years, but after a while they corroded, providing intermittent voltage to the pump. It doesn't like that...
3. Crane ignition shutter wheel contacting wires INSIDE distributor. Yes, as soon as this shutter wheel contacted the wires, it stopped turning and the engine died. Turned out the mechanic used the wrong size shutter wheel, too big for that -050, and after years of operating fine, it stopped.
Notice that two of those three issues were electrical...which all manifested the exact same "engine dying" situation.
I am constantly reminded of the old mechanic's saying that "Carburetor is a French word that means 'it's the electrical system', stupid" Found that gem in a repair manual on an old [British] Austin/MG car we once had. Those SU carbs, weird as they were, rarely failed, but boy oh boy those Lucas electrical systems...So, always think there might be an electrical gremlin behind your issue!