Add another battery?
Yep for starters. Should about double what you have if you get same size. Hope your current battery is new, so newest battery will match up with what you have already. Or if you have a small battery so might want to replace with bigger (if you have room)Then the other stuff you talked about in your posting. We plan one 1 night 1 battery when it is cold. That is 1 night 1 battery, not 1 day (24 hours) that is 1 night, like 10 pm to 6 am. Furnace loves batteries.
Generator-(my term)generates elec which is stored in your battery and available to you when you turn stuff on like your furnace. If stored elec is not replaced, the stuff you want to run, won't.