Since the vinyl has separated from the foam, I would think your going to regret trying to re-use that vinyl. It only takes a yard of new new headliner material, to recover the fiber board. Why don't you just get new, it will have the thin layer of foam on the back, which is what your going to need to glue it to the fiber board. There are a few places that still offer the headliner with the perforated holes.
When I did mine, I bought new material. But I also changed my interior color. I also did a friends "Ferd" headliner that was sagging. Here are a few pics of both headliners.
https://www.yourautotrim.com/auheclvifa.html