First, Congratulations and Thanks for posting Model, Serial, Spec information! We have 4KY Spec K also. If fuel pump had been replaced by previous owner, don't know. Carb HAD been and was already fouled with gum when we bought the coach. Luckily an OP here had a good used one he was willing to part with...
I met a fisherman/camper I'll call Old Joe. He was running his 4KY and it just hummed. Mine (before carb replacement) would start, and it would run as long as there was load on it. Once hot, and once load dropped off, it would stall and I could not re-start it. Old Joe told me "Every drop of gas that goes into my tank (which was the 55-gallon tank on a Ford E450 under a Class C) gets Stabilizer in it." I said "Even on long trips where you're only filling up for the road?" and Old Joe said "YES!" Since the new carb, I've added stabilizer every fill-up. I also try to exercise the 4KY regularly. But since I'm an irregular kinda guy, sometimes it's less often than monthly. Nonetheless, simply faultless genset operation.
Since you buy good fuel, add stabilizer and exercise the genset I'm going with the Fuel Pump crowd on this one. The ONAN Service Manual you'll probably find is 981-0530C. The 0530 without "C" is for older 4KY's. Others here can probably post a download link. I haven't had any luck finding one today, but if you PM me with your email ID, I can send you a copy as attachment.
0530C will give you Codes, Troubleshooting Chart, and Fuel Pump Pressure spec. Code'll probably be "36" which kinda means "Beats Me" and I'm concerned that by the time you connect a fuel pressure gauge, a bad fuel pump could have cooled enough to look good again.
Let me add this: Many Marinas pump ValvTect marine gasoline. It's stabilized, disperses moisure, cleans injectors, on and on. I am a Reformed Skeptic about ValvTect! Honda engine on my Pressure Washer needed carb cleaning every few months if I forgot to run it when I used automotive regular. Adding StaBil did a decent job but the fuel lines on the String Trimmer still kept failing since it was Ethanol gas. The ValvTect available in Florida is both Unleaded and ETHANOL FREE. I believe Octane is 89. I just bought my start-of-mowing-season supply. Paid $4 a gallon while plain old car gas is $2.50. Worth every dollar, every drop. If you can get to ValvTect, by all means DO!
If God's Your Co-Pilot Move Over, jd
2003 Jayco Escapade 31A on 2002 Ford E450 V10 4R100 218" WB