We have two vintage AS and both had working fridges until we took each on its first rally trip. Picnic coolers on wheels work in a pinch - one for food one for drinks.
Tried all kinds of things...horizontal fridge, turning the fridge on 2 to 4 days before leaving, replacement coils...nothing worked and the remanufactured coils weren't available for our model fridge.
My husband did a great job installing a new fridge in our '72 Argosy. There wasn't an exact replacement for the old Dometic but he got a new one installed and looking/working great.
Our '73 Overlander fridge is presently shoe storage. My husband posted some pix of the shoe storage if you're interested.
Will figure out the fridge replacement project now that the water is running and hot water heater is working. As of this weekend! Hopefully it will work on our next trip!
Be glad to answer your questions with more serious info...will refer you to my husband...he's a pretty helpful and handy guy.
The new fridge is sooo much better than the old one so I recommend replacement even though I am a vintage purist. From a practical perspective, replacement seems like the best route if you don't want to be trouble shooting your fridge all the time.
Gotta be creative and flexible with a vintage. And of course, a sense of humor is essential.
Good luck with your new project.