If you are close to National, that would be a good way to go. In my case, I replaced the dead board for $180 with a DinoBoard, only to discover the evaporator was out too. I wish I had better understood how they work. You can test function by applying 12V directly to the heater element. If the ammonia boils but the fridge won't cool at all, it is for sure the evaporator.
Now that I think about it, I will search for a post about testing your RV fridge. If I can't find one, I will make one.
As to your other question. The self cooling coolers use a peltier style element. Poke around youtube and you can find DIY builds running at around 5 amps. If that is typical and you have a 250AH battery, it could be a viable option. You could actually run it off solar most of the time. Maybe a couple of coolers and small solar setup is the best option for you.
Jose