We had a similar set up when we went to Yellowstone in mid September (2 6 volts)
We ran the furnace quite a bit, as we even had snow one evening.
We just turned on the generator when we left in the AM (around 8AM) and let it run. When we got back, it was out of gas and had stopped and the batteries were charged. We did this about every other day.
It was a small inverter generator, so fairly quiet, and run in the eco-mode, and most folks aren't in the campground during the day anyway, they are out exploring like we were. We didn't hear any complaints from neighbors. There were other generators running in the campground as well. Maybe this was the wrong thing for us to do, but it worked for us. We were at Yellowstone a little over a week.
