I've never designed or built a loudspeaker in my life, but I do know that any material will damp resonances at some frequencies. It's also pretty well known that symmetry is not a must for speaker cabinets for performace reasons, they are done more for cost reasons.
This makes me thing that experimenting with combining different materials and/or material thicknesses and rejecting the need for everything to be symmetrical may provide interesting and useful results. Although a lot of experimentation is probably needed which is a lot of work if that means building a lot of extra speaker cabinets. I think the Russel K speakers at least try to do this, replacing internal dampening with selective bracing etc. to break up resonances instead. Maybe some lightweight material like Balsa could be used to provide some internal diffraction inside a cabinet without adding weight?
Sandwiching in different ways is also interesting, for example Harbeth veneers also their MDF cabinets with a lower cost veneer from the inside for performance reasons. I remember a Hifi World article on a Peter Comeau project, where he experimented with a sandwich of two thin MDF layers sandwiching a particle board layer. A lot of different interesting options can be found for example on this page:
https://kerfkore.com/blog/all-about-lig ... ch-panels/
Embracing resonances in an undamped cabinet is probably challenging as those resonances will make their way back into the speaker drivers. Trying to isolate the tweeter may be interesting in these cases even though damping would otherwise be avoided, as I would think significant resonances from the woofer via the cabinet would cause more extra movement in the tweeter compared to a lossy mounting of the tweeter, because the tweeter does not put out enough force to move itself in the way a woofer will.