"With my equipment in Ray's situation, I would merely have gone to bed with a full tank of gas in the 550 watt genny and left it running powering our converter until it's 0.51 gallons of gas ran out in the middle of the night. While it was running, it would be doing two things ... charging the batteries up - plus powering the RV's furnace and everything else in the RV. In the morning the batteries would be at a higher SOC than they were in the evening when the generator was started because the heavy-draw furnace would not have been supplied from any battery power during a portion of the night. Doing this about every other night would have taken about 1 gallon of fuel from the little generator every two day"
Then why not just run the genset every time you need power, even 24/7 if need be, if that's the case, (seriously). 50 pounds of generator and 50 pounds of gas and you'd be good to go. Stick the refer on solar, during the day, and on the gennie at night.