Fuel pump ?

You're definitely right that it's most likely not the relay but I would definitely check all the easier stuff before dropping the tank. Personally I would see if I can get the meter hooked up as close as possible to or all the way back at the tank. Then take a voltage reading when you have 32 PSI and when you have 10 PSI. Alternatively find a way to provide supplemental 12v power to the fuel pump. I'm betting the voltage doesn't change regardless of the fuel pressure in the system. 

You say that the pressure drops from 32 to 10 PSI under acceleration. Is that under any acceleration or just heavy acceleration? 

You said if you shut it off for 3-4 hours it behaves the same as above. Have you tried waiting until it's at 10 PSI then turn the motor off and right back on? Does the pressure revert back to 32 PSI or is it still at 10 PSI? does the system need 3-4 hours to regain the 32 PSI?

Ultimately if I had to hazard a guess I'd say your fuel pump is on it's way out. Or at the very least the pump pickup sock in the tank is plugged up. They are available on Amazon.