My first thought is the same as Dave41. The carb could be getting too hot and the fuel evaporates. Just for fun, after the car has run and gets hot unbolt the carb and leave it on the bench over...
Why do you have 2 threads going for the same problem? As I understand you bought the engine used. Did you have the pan off? What prompted you to check the oil pressure, was there a previous problem?
You don't need huge amounts of pressure, 5-6 psi. Too much pressure and you end up sinking the float. Volume is more important. We always ran a mechanical pump. If you are running an electric pump...
You should be able to find a wiring diagram for each one on line. I hate it when people chop off connectors like that but I guess you can use what ever type connector you want. I like the Weatherpak...
It does sound like maybe a clearance problem. They may have the rods and mains clearances ok but what about the aux shaft bearings or cam bearings? Could be clearance issues there. Is the head...