I think Norcold has a chart of their models that most closely match the Dometic models, but yes, there are only one or two models that happen to be the same size across the brands.
I rebuilt some of the cabinets in my 69 last winter; always meant to do it to improve a few things (I added a shoe storage space under the fridge so now I have a handy place right when I get inside.)
The original 45-year-old 1/4" ply was delaminating and falling apart. So, don't be afraid to do that, its pretty cheap and easy.
Ironically my 69 Dometic fridge still works (at least on shore power, haven't fired up the propane in ages). This is funny because some of the plastic shelves on the door are in bad shape, and have been since I got the unit nearly 15 years ago. I keep waiting for the fridge to die so I can replace it with a new one, but all the old timers tell me I'm better off fixing the old one when it goes (and if I don't, they'll by the old one off of me)