I would throw the cabinets out before trying stick on paper. You would never get a clean look.
As stated before, use a deglosser, prime, paint. Don't sand unless you have loose spots, then only on the loose edges. If paper is missing it will show unless you fill in the missing areas with something like water putty, then sand smooth. It will work but takes steps and time. May or may not be worth the effort. I did a whole set of cabinets in a DW mobile home a year ago and they still look nice.
BTW our new Apex luckily does not have this stuff. It is solid wood or at least veneer as best I can tell.