I was just thinking that if your main use of that single battery is to run the furnace, I would consider firing up the generator during those times. When I had my class c with a single house battery, I used it sparingly. Using it to run the furnace would draw more power than you can spare for other uses. What I did, was to convert the nearest outside storage area to install two six volt T-105 Trojan batteries. You might also try alternating, like I used to, such as running the furnace off the batteries, then running the furnace off the generator, after that, running the furnace off the engine, all in order to keep up the power level of the battery. But my best suggestion would be to just bundle up under some heavy blankets and leave the battery for other things like lights. Good luck.
