Has the tank vent been verified? Cap or vent pipe not plugged?
A slow pressure drop is strange, I don't see heat doing anything to the fuel lines or carburetor that would drop the pressure setting still at idle.
The heat riser would cause running issues if stuck open, not a fuel pressure issue.
You are down to the pump or the tank vent. The valves in the pump could be binding up as it heats up with the engine.
The next test should be bypassing the mechanical pump.
Any chance the electric pump is slowing the fuel flow when not running?
