I agree, if it still works properly, cools good on propane, it likely does not need replacing. A recommended mobile RV tech, would be a great choice, if available in your area. He would know things to check for, how to test them, and place for parts, for an appliance that age. Taking it, leaving it, at an RV dealership, this time of year, can be a long wait.
I had a new cooling unit installed some years ago, at a propane sales/repair shop. It took just 2 days to check, get new cooling unit, remove fridge, install unit, run it to test. Labor cost was only $200. Just for example, you don't need a cooling unit, if yours still works with propane.
Jerry