If your furnace is right next to your refrigerator why not tap the 12VDC line that powers the furnace. It should be heavy enough to handle the load.
I just reinstalled my furnace (it's right next to my fridge too) and I had about a 14 Ga. wire going to the furnace. The blower motor on the furnace draws quite a bit of current. I suppose the fridge unit will not pull a constant 15 amps but will spike up there and idle at about 5-7 amps. I am sending a link to a chart on wire size and current handling.
https://www.powerstream.com/Wire_Size.htm
I looked there. There is plenty of power at the furnace. I would maybe put a slow blow (or circuit breaker) to cover the wire in the case of the furnace blower coming on at the very same moment the fridge kicks on. Please let me know how your conversion goes. I'm interested.
Also don't look for an inverter very hard. I am sure they are refering to a system that is factory installed and would operate the microwave while unplugged. I don't have one. It's the only option I don't have.
Sudsy