The new foam can't take 90?!
One possibility if you did want to weave it would be water-based contact cement. Same type of stuff used on counter top laminate and flooring, but without the nasty dissolvy stuff.
You could just brush it on instead of spraying, then use the spreader card to smash the weave and smooth it.
Or tack it down with Elmer's water-based spray adhesive. Then give it CK's "extra love" treatment with PU glue that's continuously wiped and smoothed till it cures.