I'm having this same issue. I've tried a couple different solutions in different areas, and I think I've settled on the "best" solution. Of course best is based on what's best for you.
I've found that if I carefully cut the material along the walls and take it down in very large pieces, I can use a stiff broom to get rid of all the old foam off both the ceiling and the material. It's messy, but works. Then after it's cleaned off as good as I can get it, I use a few tacks to temporarily put the material back onto the ceiling. This is just to make sure you get it lined up correctly. Then I use some adhesive that I purchase in the carpet section at Lowes called stick and stay. I let 1/2 of the material droop from the ceiling with the other 1/2 held up with tacks and apply the adhesive to the ceiling as lightly as I can get it while still covering the area. After I get it put on the ceiling, I then carefully put the material back up beginning at the center, working my ways towards the ceiling strips. That seems to work the best and keeps the material looking original. I do have to use Laquer Thinner to clean up any mess, but it works. I also may put 1/4-round on the edges as some places I can't get it close enough to the walls. Don't use any spray adhesive, as even the best 3M stuff didn't hold mine. I think the material is just too heavy for it. And be sure to put plastic down on the floor because some adhesive will drip off of whatever you're using to put it up. It's not a fun job, but then again, I have to work for the man a long time for 6 grand.
Tom