The engine is worn out. That's all there is to it. As for the reason its running poorly when the pressure drops, the only thing I can think of is that its possible the lifters are also worn as badly as the rest of the bearings (causing pressure drop) and they are dropping when they get warm, not opening the valves far enough.
As far as oil pumps go, they are RARELY the problem. My 7000 RPM Camaro motor is running the oil pump that came new in the block in 1976. I pulled it apart and checked the tolerances, and it was well with in spec. The thrust bearings in that block were worn so badly the crank was starting to hit the webbing on the main journals, but the pump was fine.
When it comes to Chevy/GMC motors, its best to use a stock volume oil pump and focus on getting the oil to return to the pan. I opened up all the galley drains (except over the cam, I plugged them) with a die grinder and installed a windage tray/splash guard in the camaro motor.