Never use anything less than 1/2" for gas lines. Used to be in the old BOCA plumbing code.
If any crap blew into that valve, it will clog the pilot filter. Try this:
First, pull that 3/8ths gas line and feed it to the nearest dumpster. Run a 3/4" line to within 10 ft. of the Fp, then you can reduce to 1/2" for the final run. If it still craps out, replace the valve. Also, replace the pilot orifice spud if still pooping out.
The pressure at the heater 4 feet from the reg. is going to be a lot higher than at the Fp 40 feet away! Keep in mind that spec. for 5.0 wci is under full load--furnace and Fp.
Manometers can read pressure but not flow.
Ask those geniuses with the air hose if they were going to install a water separator so they don't add more water into the lines. If this is CSST, you'll never get all the water, pipe dope, and crap out of it. Just another case for replacement.
Check the vent limit cap on that Max. 325-5. Just remove it and see if it makes a difference. This isn't vented to the outside is it? Any chance they overpressurized the Fp before someone thought to install the MP reg.?