That's exactly what I was getting at, when you bled it off it started. If you can reproduce that by bleeding off the air, then your IP is most likely fine, just have to find the air leak. It could be anywhere from the LP back, on the suction side. You have a 23 year old fuel system with metal lines that contains plastic and rubber o-rings that has been exposed to ULSD. There could be multiple air leaks to include a hole in the metal line.
All that said, now you have to find the air leak. If you can rig a temporary fuel tank to the LP, like a small boat tank, this will test the LP. Personally, for under $50, I would just get a new OEM style LP online. By the time you rig a test, you have spent a good part of $50 unless you have enough stuff laying around. Next, pressurize or vacuum test the line from the LP back to the tank. If you don't find it there, then it is in the tank pickup. There is a hard plastic line that runs to the bottom of the tank pickup. If you put an electric fuel pump near the tank, this will pressurize the line and show any leak, but it will not fix an air leak in the OEM LP unless you bypass it. Also, it will not fix a leak in the tank pickup line.
If you eliminate air and you still have a problem, then it is the IP. I had an air problem like this a few years back and I replaced the LP, then new lines and the tank pickup. My IP was bad as well, but the IP would not push any fuel to the injectors. I figured the air leak caused the IP to go. We were towing heavy and made it 350 miles before it shut down on the interstate. I didn't know at the time, but it had been starving for fuel the entire trip and I had no fuel pressure gauge. When I started fixing it, changed the LP and could never bleed out all the air bubbles which lead to replacing the lines and tank pickup. Two years ago, started having this problem again; found a rust hole in the bottom of my after market fuel water separator. I guess it did it's job, just need to change out the water separator filter more often.