I've got a 07 f250 with the infamous 5.4 3v 217k my issue is running at idle or on a flat surface with little acceleration it runs good with 40 psi of fuel put it under a load or climb a hill after it warms up and it drops depending on throttle position at wot it drops to 3-5 psi and misses new parts include plugs, coils, injectors, fps, fpdm, fuel filter now I'm out of ideas I even pulled the cats with no change now if I throw it in neutral shut it off wait a second and restart it'll run good again for a few minutes I'm assuming something's getting hot and pulling my fuel pressure but what could it be is my question

 

If you didn't use a Motorcraft FPDM, it could be defective. I'd also suspect the fuel pump itself. There's a sock type filter on the pickup in the tank that could be getting clogged.

 

I was actually thinking that next pull the pump check the filter i guess it could be pulling debris and dropping pressure then when you cycle the key off and the pump stops running it drops whatever it's picking up