Best thing to do is fill the stands 2/3 or more with playground sand. Otherwise, placing many strips of dBNeutralizer sheet w/adhesive along the sides would be beneficial. Rope caulk could be used similarly to very good effect. Best thing is to fill the stands with playground sand, though. NOT lead shot, though a 50-50 blend of lead or steel shot / playground sand would do very well.
The supports ringing when tapped does not necessarily indicate any problem, as nobody would be tapping or banging on the stand while you're listening to music. Such tapping makes energetic, acute vibrations that travel readily through rigid materials; besides ringing, can cause microphonic distortion in capacitors and other sensitive electronics. Airborne soundwaves on the other hand tend to be less intrusive, being more obtuse in nature and not as invasive to solid and rigid materials. High-volume SPL's can likely set the stand supports to vibrating though, depending on the acoustic environment. If so, filling the supports partially with playground sand will tame them substantially.
Herbie's Audio Lab