I would try heat setting only as a last resort. If you do try heat, definitely press from the back and try to look for a fusible that will work with lower heat for a longer period of time. First I would research glues that remain flexible and work on multiple surfaces including plastics and fabric. Maybe an epoxy?
Edit: Google Loctite vinyl flexible adhesive. I think that is what I would try.
Last edited by Prism99; 11-02-2018 at 08:52 AM.