Is there a grade or type of paper that will take glue without wrinkling? Most of the question is in the title: I'm trying to find a kind of paper that I can slather in wet glue without it wrinkling. 

I've seen this question - How can paper be glued to cardboard without creating wrinkles? - which suggests either giving the paper a coat of acrylic or using spray adhesive but neither is ideal for me.

I'm hoping to produce something at scale, so spraying individual sheets isn't a great option. And I need to paint the glue on, so spraying it is not an option. I'm currently using PVA but if there's an option for a wet but non-wrinkling glue, I'd accept that.

Presuming there isn't, is there a kind, weight or grade of paper that will take glue without distorting? High-quality paper is expensive, so I'd rather know up front what to go for rather than experimenting.
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 )