Kal: thanks for your response, I did indeed google Auralex, thanks for reference. I wish my problem were as simple as a resonance, which would manifest itself, perhaps, as a booming or suckout in certain frequency bands. My problem is more across-the-board, covering a broad swath of bass frequencies. This is a hybrid speaker design where the electrostat panels really depends on support from the woofer/bass subsystem, which it is not getting unless I put the towels underneath.
Note that I have been talking to the manufacturer of the speakers and I believe my issue is... unique and not something pervasive. But we don't know what is going on, it's apparently very odd behavior, and any ideas anyone might have would be greatly appreciated. One theory is that the two bass drivers in each cabinet have been internally wired out-of-phase, but given extensive factory quality assurance, this is seems highly unlikely.