Materials to reduce sidewall flex & vibration ?

You could certainly go with granite, finding a really good installer to cut and glue the sides and top. Corian could certainly be tastefully done as well.a bit easier to do a cutout in the front for the speakers as well. If it works really well you could start a business.

Hard floor tiles! The thicker, heavier type without self-stick bottoms. They add mass, which lowers the cabinets resonant frequencies, and damp that resonance.

Texan Sonic dampers for speaker cabinets and subwoofers are, alas, no longer available. The problem with trying to use materials to damp the cabinets resonance is that almost all if not all materials trap as much as absorb. That's why Tekna Sonic dampers were so effective, they were a mechanical diode. They were also excellent for use on room walls as it tuns out. I used to use Tekna Sonics for my isolation stands way back when was big customer. IIRC I bought the last Tekna Sonics available from Music Direct eons ago.

You know I've thought about this off and on in the past and wanted to come up with a cheap DIY that would test if it would be worth pursuing.  I came up with one idea.  If you can imagine a bag of sand (or better lead shot) say 12" long 3" wide and about 1" thick - now sew as many of these together (kinda like a bullet belt) as required to drape over your speaker's top and sides.  Now the back wouldn't be covered unless you made a belt for it, but this method was only just a test I could easily fabricate and try out and would only be applied during listening sessions.  It's not a very aesthetic thing but it could work I think.

If appearance is not a concern, a C clamp attached to each pair of opposing walls. One top-to-bottom, one left-to-right on the upper half and another on the bottom half, and one front-to-back, between drivers. Kind of drastic, but it would certainly reinforce the enclosure and prevent flexing of the enclosure’s panels, It would also simultaneously raise the resonant frequency of each panel and the enclosure as a whole.