Can I charge the house battery with a generator in an hour

No again and one battery, no matter how big it is won't power your furnace which is a juice hog. Fridge and HWH yes, Furnace added, no and don't plan on using anything other than lights either

I run 2 Group 31's and I still run my genny every eveinng for a couple hours on econo mode (inverter) and it never tops off the batteries. I might get to 80% charge, thats it.

I understand your reluctance to run the Onan. It's a 3600 rpm screamer = noise.