Depends on what type of headlining is fitted. Here in UK, Stypes were generally fitted with," West of England cloth", some later ones and the 420s had a bri_nylon type which was foam backed. There is nothing you can do with these later ones as the foam rots and the bri_nylon simply drops off. It was a common problem and tended to happen after about 10 years, not just to Jaguars.
If it’s the West of England cloth type, you could take off the side trims, peel it off and re glue it from inside the car with spray adhesive. You would really have to remove the seats to get proper access.
The piece around the rear screen area is glued to a Hardura moulding which tends to warp. This is held in by clips and should just prise out.
Only the front screen needs to come out, (I think), and normally it isn’t too much of a problem putting it back in providing you can reuse the original screen rubber. From my experience the remanufactured seals are usually all wrong and made from too hard a material. Also getting the chrome trim out without bending it and refitting it, and getting it to stay in place is one of those jobs which is in the nightmare catogary!
Pity your not in UK. I have a spare screen in my loft plus the chrome trim. These parts are the same as the MK2, so not that rare, but the rear screen isn’t.