North Carolina is not Hawaii in January. Not by a long shot.
I've measured furnace fans the drew 7-10 amps. Running the furnace from 6 PM to 8AM is fourteen hours of furnace - in operation. How many hours it is fired is another story. Add other hotel loads. Lights, water pump for NASCAR grade showers, TV or stereo and suddenly a 200 amp hour capacity bank is going to look like a pipsqueak. 250 amp hours minimum rendering a safe 125 amp hour reserve. But this is cutting it too close. Races mean partying and partying means burning lights sometimes to midnight and beyond.
IMHO brute amp hours is a crucial figure here. Three hundred total amp hour capacity suddenly seems rational. This of course is assuming a decent converter will be recharging the bank. I've seen too many instances where garbage converters took 30+ hours to replace most of the withdrawn amp hours. It would't be nuts to claim a run-of-the-mill factory converter would only recharge 3-100 amp hour batteries to 80% in 5 hours gen runtime. Whoopee! Now a 300 amp hour bank has 240-amp hours. Of which 120 are useable. These are points to consider. There is little question AGM batteries would recharge much faster but this means a real budget buster purchase. Three group 31 AGM batteries.
Points to ponder. For sure. A veritable ocean of variables.