I did similar restoration. I just soaked the trays in water until the glue came off and re-shaped the dings back into place. Picked up a half a yard of purple velvet at a fabric store for a couple bucks. Gave the trays a light cat of Elmer's. Done.
Thanks for posting that Kinge. I was just about to look that thread up.
I would try to save the original metal trays if you're able. Use a dremel with a wire brush and try to remove as much of the rust as you can. Toss the old fabric. I used flannel from Allen Edmonds shoe bags for my restoration. I also used spray adhesive to secure the flannel to the trays. The metal trays would have been held into the case with shellac. That didn't cement them in so as to be irremovable, it just sort of tacked them in place. You could use hot glue or a drop of super glue for that. You may find that the trays will snap back in and hold well enough on their own without any glue.
Post some pics of the restoration when you're done.