Materials to reduce sidewall flex & vibration ?

donjr, that's correct; and I would say at least 95% of cabinet sidewalls flex.

Cabinet flex was/is more of a concern with old monkey coffins. Its pretty much non existent in todays narrower speakers with more emphasis placed on cabinet designs, thicker baffle and walls constructed from superior material, and internal bracing.    

Eliminating resonance by minimizing cabinet flex will improve sound, more or less. But I think your approach is all wrong. I go about it on the inside with hardwood dowel. Or by thickening wall density by laminating similar material to existing. Or some of both.    

 

Thats why I suggested dowels, they take up less internal vol.. If I were to add sheet it would be on the outer sides. Dowel braces may not decrease internal volume whereas you can hear any difference. I found this to be true, although results can and often do vary. You could also think of it as the lesser of two evils.

Whatever measures are taken if the scales happen to tip far enough I might even consider making new boxes with more volume to compensate for planned bracing, thicker walls, mdf or hdf.

You may wind up doing that sooner or later anyway. Until then no experience is bad experience here.

Threaded bar with poly locks is a great idea.  

Baffle diffraction would be another concern if the widths or edges is altered. Or by using stone or composite tile, that sort of thing. Even slight changes can negatively effect how well the speakers image.