Yes a 12 volt compressor fridge is spendy.
But they use half the electricity, meaning you need half the battery capacity and half the solar needed to power a 120vAC dorm fridge, and you don't need a high wattage inverter running 24/7 to power just the fridge.
My MSW 800 watt Inverter has a standby current of 0.9 amps. Meaning just turned on, powering nothing but the annoying fan, it is consuming 0.9 amps each hour
My Danfoss powered 1.8 cubic foot fridge rarely exceeds 0.9 amps per hour.
Thermoelectric fridges Consume ~4 amps per hour and can cool to only 40 below ambient
Copper is expensive. To properly feed a depleted distant battery at back of vehicle will require fat cables, when properly terminated and routed, will likely exceed the cost of the battery. Keep wiring runs short and fat. The shorter the less fat they need to be.
12 V chest fridge Smaller fridges use less battery power
google westyventures parts for better price with free shipping. Tis where I got my frontloading Vitrifrigo.
You can occasionally find 12v compressor chest style fridges on craigslist. They get snapped up QUICK, and you can sell it there when you are done using it.
You will ultimately spend more trying to power a dorm fridge