Is there a grade or type of paper that will take glue without wrinkling?
I have some experience with these materials. Paper made with cellulose absorbs the water from the glue and wrinkles. You can try using styrofoam glue or other alcohol-based glue, this way the paper will not soak up with the glue. You just need a thin layer, if you apply a lot of glue the paper may wrinkle. This glue is wet, transparent and allows the use with a paint brush.



Additionally you can use paper made with cotton. I use this kind of paper to paint watercolor and I layer lots of water on top of it. Make sure the paper you're going to use is 100% cotton too! (there are 60% cotton / 40% cellulose watercolor papers that are not that great )