Tricks for Sagging Headliner?

[Mapearso]

So the original headliner on my Cheyenne Super is sagging pretty bad... and the trim around it is kinda warped.

To fix the headliner -- I assume I use liquid nails, some good 3M adhesive or some VHB double-sided 3M tape?

To fix the trim -- Not sure? It looks like I could add a couple of screws to the area where it is warped the most. But the truck is really stock and unmolested so I dont love the idea of putting a handful of holes in it that weren't supposed to be there

Any suggestions are appreciated!