Experiment #2 (Update)

I tried using an old Windex bottle to spray watered down glue, which sort of worked, but I wasn't able to coat the whole sheet yet and the bottle is ruined. Dipping and wringing the sheets soaks up too much to be cost effective so I'm hoping to find a spray bottle that I can use with better results.

The sheet is fairly hard, though I'll probably need to coat it twice to get it to a desirable stiffness.