Shane:
   I'd suggest using a contact adhesive such as that used for plastic laminate
(formica).  It is available in small aerosol-type cans, ideal for this
application.  Be sure to mask off areas that shouldn't get glue on them - it's
a bear to clean.  Spray of brush the adhesive on both surfaces to be joined,
let it dry, then press the two surfaces together, being sure to bond all
sections by rubbing.  The pros have a hard rubber roller.  I've used blocks of
wood, my hand, whatever.  I've used the adhesive to reattach the carpets where
they came loose around the wheel wells, too.  Most hardware stores should
carry it.

Regarding the paper, I'm planning to replace my peeling paper with plastic
laminate.  There is an almond colored laminate that matches the Westy's
cabinets exactly.  My door panel was trashed by the DPO when he tried to
"tighten" the outside handle.  I'm in the process now of making a replacement
out of thin (3mm) plywood with the almond laminate. Additional advantage:
smooth, easy clean surface!

The buttons should be available at your FLAPS, though I don't think you'll
find them with the texture of the originals.

Good luck!
Doug