Ooof, I struggled with this on a couple VPI setups in a "tricky" room / floor scenario. The feedback sound can range from an audible rumble to very much like a ground hum (but not one). Definitely NOT the motor. It only emerges during high volume levels (and increases with it), and it can possibly hit a "runaway" threshold.
Best I can surmise, it’s the plinth and arm (or particular materials & design) which are energized by these frequencies. Interestingly, the metal VPI unipivots had significantly less feedback than 3D wands or Fatboys. Most footers (rubbers, polymers, hard cones, etc) had almost no effect. VPI’s HW40 footers with the really squishy / compliant foam layers had some positive effect, but didn’t fully solve the issue.
Clearaudio’s Innovation with the magnetic bearing didn’t have humble / hum feedback issues, but had the woofer flapping (subsonics) PLENTY bad (which the KAB filter does solve) - haha, what a torture test for tables here in my office rig!
I’m surprised your attempt at springs didn’t solve it? But they must have been the wrong springs / wrong loading or tuning. That’s the magic of SOTA’s internal suspension - in the same room & setup, NOTHING gets past my SOTA Cosmos. No problems at any level of playback. Of course, I don’t run a sub and that will pump plenty of bass back into the system. And you still need to ensure you don’t excite the suspension during playback (rigid rack mounting - you’d be surprised how easily most racks can sway enough to matter).
I think a Townshend platform or pods with the right load rating would solve your problem, but they’re a bit spendy - but then they’ll be way better here than some of the much more expensive "constrained layer damping" audiophile platforms. Which are generally pretty useless for "macro" scale problems like this.