The OP has at least 216Ah's. And a furnace blower cannot go thru 108 Ah's in one night, unless it's running continuously... which it is not.
After "charging" for 12 hrs, there is no way a 216Ah bank can be anything less than full. And by charging, I mean charging... not trying to float the batteries to full with a converter at 13.6v. If you're gonna boondock, you need a real charger, not a converter set to 'normal' operations. I can charge one of my 215Ah banks, from 50-95%, in less than 4 hours with a 60 amp charger.
Having to turn the heat down to 45F, and run the genset for 12-24 hrs a day, is absolutely absurd, and completely unnecessary.