Get a true water pressure regulator as you mention - it’s the only way to get a true idea of where to start looking.
Our ‘02 coach also seemed to struggle on water pressure when hooked to the park system. I ended up replacing the inlet connector with the integrated check valve.
They can be serviced but they are a pain to do so. As cheap as they are, you buy a new one, replace, and move on.
BTW - when you get a regulator with a pressure gauge, always read and adjust the pressure with water flowing from at least 1 faucet.
‘91 Ultrastar Champion‘02 Georgie Boy Landau 8.1l Workhorse
‘03 Jeep Wrangler TJ 2018 Jeep Wrangler JK toad