I had tried not to sound too negative, but I agree in that I have never seen anyone "save" the headliner material (used in boats when I've been dealing with it).
Like Gus says, if it were me I would rip it off, clean off the adhesive residue, and then go from there.
You could just paint
the bare fiberglass walls, or re-install open-celled foam, but If it were me, I'd use Ensolite. I know you won't be camping in cold weather, but it also helps to insulate the trailer in warm weather, and, unlike the open-celled variety, it seems to hold up for a loooong time. (I've looked at a lot of 1970's trailers with Ensolite, and unless there was something catastrophic like fire or water/mold from long-term, unattended leaks
- or some other specific disaster - the Ensolite has always been in good condition.)