I have built up, used and sold a few 4 to 6 battery invertor packages to friends with off the grid cabins. These have the ability to run most anything residential in nature including a gas furnace. I am gathering materials now to build an 8 battery multi inverter bank and genny package. This is an expensive build but when done it would have the capacity to run 2 houses if properly monitored and usage was kept under control. A fridge like OP lists would not hit that bank very hard at all.
I am looking at solar options to keep the banks topped off but that ain't cheap either.
I am looking at solar options to keep the banks topped off but that ain't cheap either.