An 04 doesn't have the failure prone "STC" fitting. Only 05 and up.
With over 300k miles, I am surprised that the HPOP is still good (assuming it is still original).
Air test it.
Thanks Bismic, it is the original pump. After a few weeks of not being able to work on it from just having waaay too much other stuff going on, I finally got into it again yesterday. My brother-in-law and I pulled the HPOP and used my air compressor to test it as you suggested - like in this video:
The pump in the video appears to be a newer style pump, but I think the idea is the same. Anyway, so I think the HPOP has gone bad. It wasn't as obvious as the one in the video, but when we put air on the output port and a finger over the inlet port, and turned the wheel, we'd feel air kind of popping out the inlet port. Though not freely flowing, air was definitely moving the wrong direction through the pump. On a good HPOP there should be zero back-flow through the pump regardless of if the wheel is turning or not, right?
Thanks again everybody!
2004 F350 6.0 PSD, Long Box SRW Crew Cab FX4
Completely stock, minus the EGR
320,000 miles so far