Nitrous plumbing A1A...??..

All set ups are different of course, I wouldn't necessarily worry that much of FP going below 5psi, I tried 4psi once from 6 on my rather rich cheater kit to see if ran faster, picked up a very small amount, I had a separate pump like you and my press was rock steady always, surprised yours goes down. Also short Fuel line and long N20 line is GOOD.
Yes of course if it goes any lower than 5 the low fuel pressure switch one cut the ground to the solenoid and everything will shut off. Also my first setup had a really messed up setting put that Speedmaster junk. It had one short and one long fuel line and one short and one long nitrous line LOL.. I got that all fixed now it has two short lines going into the center for the fuel and two longer lines going into the nitrous from the outside..
Just waiting on the bottle heater now. when I tested the nitrous oxide out yesterday the pressure was only like 700 or so...