When you say you "charge the chassis battery with the engine running, and after shutting it down, the battery holds a charge." That is probably a 'surface charge' and isn't a true indication of the battery's state of charge. Check water level in battery cells, then put it on a battery charger overnight. After unplugging the charger, let the battery sit a couple of hours and measure voltage. A fully charged battery should be at about 12.6 volts.
You stated it's not a fuse problem, but it could be a circuit breaker that automatically resets. Do you have a Chassis battery cut off switch? You stated you used the 'generator crossover switch' which I think you mean a battery boost switch on the dashboard that inner-connects house and chassis batteries while you hold it down, often called a boost switch.
You didn't identify the RV chassis maker, but I guess a Ford. Look under the hood for a plastic box that contains fuses ane solenoid relays for chassis functions.