Like I said above I'm fairly certain the engine will run with the rail sensor unplugged so don't mess with that

the codes lead me to believe that your problem lies with the FPDM circuit; it could be the ground wire to the frame at the FPDM, or the connector to the FPDM is not tight. Remove the gasket from the connector and see if it has a better connection. or you have some wiring that's bad or corroded in the fuel pump/FPDM circuit. Like under the plastic guard that's in the frame rail under the driver's seat dirt/corrosion at that connector is a known problem as well.

 

When you unplug the rail sensor the duty cycle for the fuel pump goes to 100 percent
Monitor the pid with the sensor plugged in