Hi!
Many years ago, When I started this hobby I used to fish B.B. damaged models out of a fountain. After cleaning I would use fine typewriter paper and Tenax or Testors liquid glue. Holding the paper tight to the surface created a perfect weld. No one realized after painting that I had repaired stuff that way.
Now for what you are doing I would use one of the contact cements that is thin enough It doesn't leave any lumps. I have run across a "White(Clear Glue) in a kit I was given that does the same thing. I don't know what it is, But, you may find it at Hobby Lobby!
I did an experiment lately. I bought a package of paper at Dollar General. After testing it's permeability I tried it on a test hulk I have. The results were very gratifying.The cheap paper soaked up the glue and stuck nice and permanently to the plastic.After set-up and that took at least two days.I sanded(YES, sanded the edges) and painted with an out of bottle MR.Surfacer 500 primer/surfacer with 600 grit WET. I then put on a finish coat. I Couldn't tell there was a difference in plastic material and the paper area, where I had removed plastic behind, before applying the paper!