Frankly I don't understand the paranoia surrounding leaving a furnace on. All over the country there are houses with gas furnaces and gas water heaters (including ours).
There is not some magical difference between the burners in an RV and the burners in a house.
FWIW, I leave a small electric heater on in the RV because I have shore power available. If I didn't I would fill up the tanks, set the furnace as low as possible, and try and position in a sunny spot to get a much solar charge as possible for the batteries.