Residential vs Gas/Electric Fridge?

After a set back in our plans, we're back on the trail looking at fifth wheels. I think my last question comes down to which type fridge? We'll have some solar no matter, but since we're looking at a 35' trailer and we'll be doing National Parks and Forest Service Campgrounds, I am thinking we could do a residential fridge.

What I am trying to figure out is whether we could run a residential fridge on an inverter and a couple 100ah deep cycle lithium batteries for a week or so?

Combined with some solar charging and a small portable generator to help keep the batteries charged up.

Any thoughts on which type of fridge you'd recommend?