We have had the peeling paper veneer problem on 3 doors…bedroom, half bath and main bath. I have tried using contact cement to stick the peeling edges down, and it works, until the paper next to the glue spot starts to peel. It drives DW crazy.
For the large piece of paper in your first pic, I would definitely try the contact cement…put the cement on both surfaces, let it dry 20 minutes or so and stick it back down. I keep a jar of Elmers Contact Cement in my tool box. It has a brush on the cap.
I don’t think there is a way to correct the issue or prevent it from continuing.
I suppose they used inferior glue in the Keystone factory. I also own a 2004 Fleetwood motorhome with paper veneer on some of the cabinet work. I have ZERO issues with peeling paper veneer on my 20 yr old rig.
Edit: we have used thes furniture paint pens with some success to touch up dings in the woodwork in both the Montana and the motorhome. At some point I plan to glue the edges of the doors as best as I can then use the paint pens to color the exposed MDF edges to match, and just pretend that the problem is not there.