53Chevy -
I feel your pain. I have the same issue, except my pump works intermittantly. It pumps normally for a while, then seems to lose its prime and stop pumping altogether. When the pump is working, it works very well. Plenty of oil to the rockers. Then it suddenly quits, as if the engine were turned off.
I believe the pump has a pressure relief valve on the side of the pump. If the valve is stuck open, the oil pumps straight back to the pan instead of the rockers. I've concluded this is my problem, but I can't think of any way to test this theory short of replacing the pump. Of course I didn't discover this issue until the engine was installed in the truck, so changing the pump is not a simple matter.