I remember Madisound carrying a very expensive Scan-Speaker woofer with a short coil/long gap geometry. I recall a peak-to-peak x-max of about 10 mm, or 5 mm one-way. I think this was a 12" woofer, but maybe yours is a larger version using the same motor.
Looks like the box volume is about 20 cubic feet.
The "variovent" is not a port; rather, it's a pressure-relief device. The use of variovents actually decreases the very deep bass output and/or increases cone motion relative to a sealed box.
Anyway going back to my over-excursion theory: In a prosound application, the woofers were probably protected against being overdriven by a high-pass filter which filtered out signals below maybe 32 Hz. You see, in a sealed or aperiodic enclosure (which yours is, with those vario-vents) the excursion-limited output at 32 Hz will be about 10 dB higher than the excursion-limited output at 20 Hz. So by protecting the woofers with a high-pass filter, a lot of headroom can be gained.
If the woofer's motor is indeed of the short-coil/long gap ("underhung") topology, that's usually very linear up until the point that x-max is exceeded. Once that short voice coil is excursing beyond its linear range, distortion goes up very very fast. My guess is this is what you heard.
You could increase your excursion-limited maximum output between 30 and 20 Hz by perhaps up to 10 dB by replacing those four variovents with four 4" diameter ports each 5.5" long, but the result would probably sound too boomy unless you could equalize it. If you have a suitable equalizer, that might be the way to go. Otherwise, I suggest some sort of high-pass filter to protect the woofers against over-excursion. Unfortunately, I really don't think an increase in damping material is going to solve your problem.
Duke