From the OP:
The problem is, the overall sound can vary vastly from lean-strident to round-warm very quickly based on what kind of spike base I use underneath the rack.
Most of the comments above, including Halcro's insights, assume that the sonic character of Pani's table varies with the spikes beneath his rack because the spikes provide different degrees of isolation from floor-borne vibrations. While such vibrations certainly exist, in my opinion they're not the main source of what Pani described. Other vibration sources are more likely to produce the described effects.
The other gear on the rack is a noise source, both from its native vibrations and from the musical energies it's reproducing. The turntable motor is another noise source, and some PV motors are notoriously noisy. Stray energies leaching from the stylus-groove interface are the most influential noise source of all, since they're closest to the pickup.
These noise sources produce stray energies in the audible band, not just at 2-10Hz, and they're physically and acoustically closer to the TT than vibrations from the floor. The footers beneath a rack have a profound influence in a setup's ability to drain these vibrations away from the TT - or not.
Reducing stray energies in the 2-10Hz range will lower the system's sound floor, but it's unlikely to change the sound "from from lean-strident to round-warm" or vice-versa. IMO, such changes are more likely due to changing stray vibrations in the audible frequency range, such as are caused by the factors noted above.
That said, a wall mount such as Halcro suggests would address both structure-borne and equipment-borne vibrations, as it would isolate the TT from both. They'll have less effect on TT motor noise and vibrations emanating from the stylus-groove interface, which must be addressed by other means.
It's far from a simple problem and there is no single solution.