Do these Onan gensets have a good fuel filter? Is the tank steel or plastic?
I don't have a dog in this fight but am always curious about small engines. From postings on this Forum I know the replacement of the carb is the typical fix for fuel related problems and some folks seem to have a rash of them. I've had my hands on more than a few fuel systems and constant fuel related problems typically is related to tanks or the quality of the fuel.
Also, I seem to recall that the OP had a failed furnace so was thinking about running the genset while underway, powering electric heaters. I don't know if that became SOP but is a sure fire way to stir up any residue in the tank and consequent carb problems.
The bit about the lying A-hole mechanic is just the reason I ended my career as a wrench turner. I wasn't too happy crawling around under someone's rig just to be treated like a thief when the work was completed. My suggestion would be to buy $5K worth of tools, tune your memory to remember more parts than a Doctor, douse yourself in petroleum, and perform some of this work. BTW, be prepared to be treated like a thief because your customer doesn't understand how things work.