using spray glue and contact adhesive on the original lining does not work, from experience!
my advice would be to remove the headlining (a ballache but necessary), remove the vinyl lining and any traces of the old foam from the backing. then re-cover the backing with acoustic carpet (thin/light enough to not come away from the backing).
carpet glue or contact adhesive should work, make sure its set before you stick it back into the car though