Yep, a furnace eats up a ton of power. The old saying is "one battery, one night." I really don't understand why they can't put a more efficient heating appliance in an RV. Not only is the standard gas furnace an electricity hog it also seems like it's wastes a lot of heat. Ever felt the air coming out the furnace vent? It's sometimes hotter than the air coming out the ducts inside. Seems like a terrible design that hasn't changed since the 1950s.
I'd probably just run large wires from your current battery compartment to the new location but #4 isn't nearly large enough for a 2,000 watt inverter. You would want something like 2/0 for that load; it's likely to be around 200 amps when making 2,000 watts.
If you decide to put the batteries back in the exterior compartment then it's really easy to put them back. I know space is tight on a TC, you could put them back outside all summer and they would probably do quite well.
Really, I'd probably just try to get a second battery in the same compartment and keep in mind that you will need run the generator every winter morning.
