Every so often comes a post asking about cheaper refrigeration on battery power.
Ther thermoelectrics are always asked for first and dismissed for being inefficient, ineffective power hogs in most every situation.
Next come the 120Vac dorm fridges run on an inverter, but these will consume at least twice the electricity as a 12v compressor fridge and require a larger inverter, battery bank and solar or other recharging sources, negating the price difference between a 12v compressor fridge and a 120v dorm fridge.
Now if one already has a dorm fridge, and an inverter, and a surplus of solar or other recharging ability, then go for it, but do not seek out to run a 120 $ fridge which requires 500$ worth of batteries and solar panels to run indefinitely.
Dorm fridges might also suffer failures from road vibrations, and one needs to design a method to hold the door closed as well.
Long story short, if you want electric refrigeration and live on battery power, then a 12v compressor fridge is the first and last stop, and efforts to beat the system, will ultimately be defeated, as it is simply easier to use less electricity, than plan on generating huge amounts so one can be wasteful running an inefficient appliance.
Bite the bullet and get an AC/DC chest style fridge/freezer or a front loading fridge with freezer, and plan on having at least 60 watts of solar dedicated for just it, to keep it running indefinitely.