3M Foam Fast 74 Spray Adhesive Orange is what John the mechanic at DMC Northwest in Bellevue, Washington uses to attach the foam headliner fabric to the headliner boards.
It’s specifically designed for foam and it’s orange when sprayed out of the can.

He also uses an incredibly fine dental pick tool to raise the gray fabric if he accidently presses too hard on the headliner fabric while the glue is still wet. Once the glue is dry there is no way to fix mistakes except by going back to the beginning and doing it all over again.

John and Toby also converted a Left Hand Drive DeLorean to a Right Hand Drive. It is currently being prepped to be sent to the shipping docks for delivery to Australia. So they know their sheeeeet.