Thanks T-Rex!
Just for back ground, I found that my fridge plugged into my AC180 ran for 10 hours.
1150wh(the advertised capacity of the AC180)/10hour = 115w average usage, so the external batteries should be able to keep up within the 10A/400W limitation. I would run 4x 12v batteries gives 4800wh. 4800wh/115w = 41.7hours + 10hours (internal battery) ~ 51hours (so call it 48 hours) maximum run time on my fridge without recharge.
Haven't thought about the solar end yet, but it shouldn't be too outrageous.
If we are going to all that trouble (same batteries, solar panels and solar charge controller), add a 1500w inverter, cable, fuses and switches, you would come out a few bucks ahead. (But you and I already have the AC180, so we'll use them as a starting point)