"the gears being too deep in the pump body to the surface where the cover plate bolts on being a source of a pressure leak"

Yes, examine this, should have no more than .0025" end play between the top of the gears (pump upside-down) and the inner face of the cover, with a used gasket of known quality (not a piece of paper).
If it's significantly more than this (over .003") you need to remove depth from the body casting. If you have a steady hand you can lap the end on an old mirror with valve grind compound (I make "figure 8"s). Surgically clean after!
Do not tighten the cover screws to more than 9 ft./lbs.

If, as said, it's loose bearings increasing the idle speed even 100 RPM may bring the pressure up. Otherwise I would try increasing the oil viscosity slightly. Not straight 40!