Patching and Plastering - Drywall Paper Wrinkling / Lifting - To Be Covered By Tub Surround

We removed our old bathroom tub surround leaving the drywall behind it with a layer (or more) of paper removed because of the old adhesive. We pealed most of the loose paper pieces, but small remnants remain. I had to patch numerous parts of this area with drywall mud, which caused my problem.

The mud causes this paper area to produce many wrinkled / lifting areas where the paper lifts from the drywall sheet. My concern is that the new tub surround adhesive will pull away from these areas as they are not solid to the drywall. Thus the new tub surround (http://www.maax.com/en/Products/ProductInfo.aspx?CodeCategory=B&Brand=7&ProductType=8&Product=804) will not be total secured to the drywall.

Should I cut these areas out with a utility knife and then prime the other exposed paper areas with a sealer/primer? Will the primer sealed produce the same effect? I think I will test an area to see if the primer/sealer will do the same thing as the drywall mud. I don't want to have to install new drywall if I don't have to. The drywall is solid, but the paper is the problem.

Any other ideas?

Cut out the loose paper and then coat those areas with a solvent based primer. The moisture in both mud and latex primer is what causes the compromised paper to wrinkle.