Materials to reduce sidewall flex & vibration ?

pass
Seriously I would take out the woofer, which is the drive that usually causes most of the large back waves, and just stick some modified bitumen in the side and back panels. Self sticks, easy to cut to sizes. 
You will be crating a composite panel speaker. These bitumens I am referring to are often found in speakers and in electronics. Stuck to the inside. 

creating a composite panel speaker

The answer is obvious. Smart metal. 

cascade spray

Thanks johnk but the damping spray you mentioned,although it does have its application benefits, will not contribute to my goal of maximizing rigidity..  "I'm curious about fiberglass and other products that can attach/bond permanently to the sides yielding the highest stiffness to weight ratio." So far my research seems to indicate that epoxy filled with fiberglass or carbon fiber,or carbon nanotubes, combined with high mass material is the best option. I continue to research and appreciate contributions.