Materials to reduce sidewall flex & vibration ?

Well the gold standard is carbon fiber. Expensive and hard to find it what it does is absorb the back wave  and convert that energy into heat. Saving that I would look at bitumen, or modified bitumen. They are often sold as a water proofing membrane that is played under shingles. Soft and sticky it can be cut to size and attached to the inside of your cabinets. 

Maybe ceramic tiles?  Rigid, kind of light, and pretty inexpensive to try.
 
And the speakers would look right at home in the bathroom!

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.