Fuel pressure should change a little with engine vacuum. Pressure should be higher with the engine off (no vacuum) than with the engine running (high vacuum). When you give it gas, the fuel pressure should increase (low vacuum) then decrease as the vacuum increases. It might be interesting to hook up a vacuum gauge to see if the fuel pressure changes coincide correctly with the vacuum changes. That said, it really sounds like your fuel system is not keeping up with engine demand -- I can think of no good reason why the fuel pressure should drop off as you goose the engine. With a new AC Delco, pump and a new fuel pressure regulator, it seems appropriate to assume those components are functional (though we may want to revisit them if we don't find a better reason). How about voltage to the pump? New pumps that I've seen almost always come with a new wiring harness to "repair" any wiring damage sustained to the harness. Excess resistance in the wiring to the fuel pump could cause the pump to run weak. It might be time to go over the fuel pump circuit very carefully to make sure there are no weak spots in the wiring. You did change the fuel filter with the new pump? Any sign of damage/plugging/restriction/kinks in the fuel supply line?