Fuel pump running constantly wont actually do anything other than circulate fuel round and round as the fact the injectors shouldnt be opening means it'll all just flow back via the return so this doesnt really tie up with overfuelling directly. Im not sure what the trigger is on the FRST prime, whether it stops due to the pressure being reached, or its just a short prime via relay. As you've swapped the relay out, i guess its gonna be check the pressure is being reached and/or trace the wiring. If pressure is the trigger, then it sounds like low pressure situation which would explain the poor performance when running