One thing to NOT do: don't reuse the original foam-backed cloth! The foam is what's rotting......
I did this on my '84 Oldsmobile back in '93. I cleaned all the foam off of the cardboard, but left it on the cloth. Followed the FMS procedure for regluing, bought the right glue, etc etc.
It looked fabulous when I was done. For two days. Then it started to peel again.
I found me some nice matching blue thumbtacks at the hardware store, and went for the "tufted" look after that (after all, it was an 80's Oldsmobile!). Then the thumbtacks started to pop out! (Yikes! Don't like them sitting on the seats!). So I pulled each 'tack, and superglued them back into the holes.
Den