I hate to be a pessimist, but how is the oil pressure?
Years back I had a pick up that leaked oil BAD. When the oil level got low the pressure would still register on the gauge, but flow was not high enough. It didn't take long for the engine to seize. After the motor cooled, it would start back up. It was hard to trace the problem when the oil gauge still showed pressure.
Maybe a piece of gasket found its way into the pickup tube or into an oil passage somewhere, and is restricting flow.
I hope that you have enough good luck, so that this is not your problem!