Most 3-way fridges can't actually cool down on 12V. It can help to maintain the current temperature better than leaving it off would, but it's really not very effective.
Evaporative refrigerators are VERY inefficient. They're several times more energy hungry than compressor refrigerators. 12V has trouble supplying enough wattage to provide useful cooling for any but the smallest. The advantage to them, and why they're so popular in trailers, is you can run them off of any energy source that provides heat, such as propane.
Leave them on propane while traveling and it'll work fine.
2014 Innsbruck Lite 198BH