I think you'd have to rely on measurements of some sort - maybe SPL levels 1 foot from the side of the cabinet - because I think you want your information radiated from the primary surface (the cone) and not some reverberant stuff "unrelated" to the recorded sound. So the issue might be that the stuff radiating from the sides of the cabinet are, say, -30dB from the level measured at the cone and essentially don't affect the overall presentation.

Maybe you could build a box with 1/2" MDF, then in succesive measurements you could laminate outer layers to thicken the walls. I'm betting with no bracing at all the cabinet will be pretty stiff after a few layers, and you avoid the differences in internal volume as well as the work in constructing multiple speakers.