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. 

creating a composite panel speaker

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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. 

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Well sometimes the most rigit is not the best dampening material. Sometimes they just store the energy and release it slowly Not good. If your speakers are vibrating, and most do, then glueing solid materials to the outside may not work out so well. The vibes might possibly loosen the rigid material right off the panels. Imagine glueing a rigid panel to the outside of a clothes dryer. 
Once they begin to loosen you really have a problem. I much prefer my recommendation. 

You should note that low mass materials resonate at higher frequencies. Ping a wine glass and you can see how that works. Now take a hammer to a heavy piece of metal. Much lower frequency. High frequencies are easier to dampen. To stop the wine glass from resonating simply touch it with your finger. This illustrates another principle important to controlling resonance and that is composite technology. Your finger resonates at a different frequency then the glass and together they work to absorb the resonance. 
You might reset your goal to making the speakers sound better by reducing the cabinet resonance. There are not a lot of speaker companies out there that do more then stuff foam in the box. A few but not many.

My final weight in. 

Buy new speakers and give up the science experiment. 

Then don't buy new speakers, buy used ones on Audiogon.