Not wanting to run the generator at night and limited to 20 amp shore power, I would do the following:
Use the 110v 20 amps to run the catalytic heaters, check the amp draw, you may be able to only run one at a time.
Run the water heater on propane.
Put antifreeze in the holding tanks, the tank heaters may draw too much current. Or, disconnect the batteries via the store switch and run the tank heaters. Then the converter will not try to recharge them and not draw any current, then recharge in the am with the catalytic heaters off or run the generator to recharge.
The rest of the plumbing is within the insulated walls and will be fine if you keep the catalytic heaters going.
Instead of the catalytic heaters, you could run the propane furnace as it doesn't use as much electricity as the catalytic.
