I never (!) saw a "mode" in a panels motion, which should be an-harmonic. The panels motion always (!) reflected, if at all, harmonic (1, 2, 3 …)modes of air resonance inside the enclosure. That is a huge difference in understanding the topic. I have to admit that quite basic considerations regarding stiffness were taken into account. E/g the walls thickness was left to be 12mm for practical purposes, as to provide some area for (sloppy) glue-joints and so on.
Today we have laser scanners and the mathematical tool of boundary layer analysis. Once You use it, it contradicts the work model of e/g the BBCs investigations, which addressed the panel alone. Comes out: non-issue, with halfway reasonable construction.
I already advertised to build a vibrometer yourselves. From a cheap and readily available electret microphone. Nobody asked back … If You build two, You could easily investigate phase for instance, as to detect--or not--differential "modes". Why is it, that everybody likes to speculate on imaginations, driving useless effort to stellar heights, while a simple device is handy in order to catch a glimpse onto the real world instead.
Consider it to be the same as with a microphone. Would You actually dare to work on a crossover without? Why do You do so for an "optimized" cabinet?
Regarding shape, this works pretty nice, and doesn't cost a leg and an arm, marriage, kids, house, dog:
https://heissmann-acoustics.de/disco-m/