Thanks everyone for your input. Here's some answers to the questions raised:
Rod side clearance is a good suggestion, but would that cause these symptoms, i.e. pressure was good at first and then rapidly dropped?
The oil pump is a high volume, high pressure Melling unit. It is new, along with just about everything in the engine. But the pickup is stock, as is the oil pan. I have a Milodon baffle at the rear to prevent oil from climbing up when accelerating.
The pressure relief valve at the pump was one of my suspects. That could sort of explain why the pressure was good at first couple of startups but then suddenly dropped while driving the car.
I will take out the engine on Thursday to drop the pan and check the pump. Any new ideas are still welcome until that.