Not sure how much your furnace is running at night but if it is running very much that of course is a significant load. What are your objectives? Do you want to go more than a day between charging? You did not give the battery group size so not sure if you even have a gr 27.
We manage nicely with a single Trojan SCS 200 (Gr 27 115 AH 12V) battery dry camping for over a week in the Smokies during chilly fall weather. We do daily morning charges and run the furnace in the evening and in the morning. It is too noisy to run while sleeping. We use a catalytic heater if it is going to be below 50.
Regardless of what battery you have you need to be sure it is in good condition and can hold 12.6 V for at least 24 hours after a full charge and no load.
Dick