With a MBM(mid-bass module), you only need to worry about shifting the resonant frequency of the panels at least 1/2 octave over the intended low pass crossover point, assuming you use at least a 4th order slope. So, if you are going to cross the mid-bass at 150 Hz, you should shift the first resonance panel mode of the cabinet to start no lower than 225Hz. You can accomplish this by using stout hardwood or metal bracing in a matrix (on x, y and z axis) internally that has spacing of no more than about 4.5"-5" from each other. This should push the 1st panel resonant frequency safely above the intended target point. The thickness of coustical dampening depends on the internal dimensions.
I recommend that mid-bass modules be used only in sealed or dipole(in case of using with an open back speaker system) configurations. Ported configurations, IMO, are only suitable for sub-woofer systems, as the port operation and it's complication with acoustical resonance(s) in conjunction with the acoustical dampening is an issue best avoided if possible when dealing with mid-range bandwidths.
-Chris