3-M 90 (super trim adhesive) is fine, but don't use 77 or 74, they will not work, cuz they're not high temp adhesives.
Yes, if you do it like I said, you should be able to get it smooth. It looks like the fabric is some kind of imitation suede. Does it stretch? If not, it will not be as easy to get the wrinkles out, but it still can be done.
No one lives forever, the trick is creating something that will.