I use the fuzzy, industrial Velcro as my rest and my side plate. It's very sticky strong on the adhesive side. I usually just stick a piece of wooden matchstick underneath the Velcro on the side plate and then push the Velcro back into place. Experiment with different thicknesses until you find the right thickness. It might not take much material to make a difference.
The Velcro does good at keeping it's "stickyness" even after several times of pulling it back and pushing it back on. You don't have to take it all the way off, just peel it back enough to put something in behind it and then push it back against the surface of the side of the bow.