How to isolate turntable from footstep shake or vibration

@esputnix, 

If you check with Oracle you will see where they have added a damping system to their sprung suspension -  Parts & Upgrades | oracle (oracle-audio.com)  MkVI Micro Vibration Stabilizer System (MVSS) upgrade; its a significant modification.  

What is likely happening is that the sub-woofer and foot-fall frequencies  are exciting a table spring resonance.  At resonance, an undamped system - in this case your floor - can amplify the vibration/displacement many times - often well over 20 dB.  So, every foot step causes the floor to effectively bounce causing the stand to bounce with it and the undamped table springs really bounce.  As has been suggested:

-a rumble/subsonic filter 'may' help because it may isolate the frequency that the subwoofer is producing that is exciting the floor from foot fall; example  Line Level Crossovers (hlabs.com).  There are pro/cons to these, but they are cheap and there are other types available - just search.

-modifying the table for the Oracle MVSS 'may' help because it now adds damping to the Oracle suspension that it currently does not have.  If it does not fix the problem, it may still benefit the table once the subwoofer/foot-fall/floor issue is resolved - but this is a significant mod that requires machining the base.

-mounting the table on the wall 'will' work; it isolates the table from the floor.

-adding a large mass under the table 'may' work.  

-adding subwoofer isolation feet or pad 'may' work because it may isolate the subwoofer from the floor enough so that the resonance is reduced or eliminated (shifts/isolates the problem frequency enough); and these are not expensive.  Examples are  Amazon.com: SVS SoundPath Subwoofer Isolation System, 4-Pack: Home Audio & Theater;  Amazon.com: IsoAcoustics Iso-200Sub Subwoofer Isolation Stand (Single) (New Model): Electronics;  Amazon.com: Auralex Acoustics SubDude-II Subwoofer Acoustic Isolation Platform, 1.75" x 15" x 15", v2: Musical Instruments.

-as has been stated - adding secondary springs under the table, is not generally recommended.  The phase relationship of the two spring systems can lead to very unpredictable results with resonances at different frequencies that can make the situation worse.  

Good Luck,

Shock/vibration isolation of avionics is documented and easily accessed - examples  Microsoft Word - avioinics_iso_revC.doc (vibrationdata.com), and compressed_PC6116_AerospaceandDefenseIsolatorCatalog.pdf (lord.com).  Exactly what shock & vibration performance the avionics has to survive can be classified.

@atmasphere,

in my prior post I should have gone into greater detail, but for the OP, when the floor bounced in the upward direction, the turntable spring went into compression.  But because the spring was not stiff enough the spring fully compressed at which point the 'suspension' essentially bottoms-out and now there is no suspension and the force is transmitted directly to the table. 

In your circumstance, I suspect that the floor is resilient/soft enough that foot fall causes a ripple effect which then has vertical force component and a horizontal force component.   Use of ball bearings to absorb horizontal vibration is well documented; ergo, they worked for you. These vibration reducers originally were developed for audio use - Vistek - Designing with Series 320 Vibration Isolation Bearings (newport.com).

FWIW and noting that this thread has taken a side route, here are just two documented sources for tube microphonics;

-Proceedings of the Institute of Radio Engineers, Volume 17, Number 9 September, 1929, MICROPHONIC IMPROVEMENT IN VACUUM TUBES  IRE-1929-09.pdf (worldradiohistory.com).

-Getting the most out of VACUUM TUBES by Robert B. Tomer, 1960,  Getting the Most out of Vacuum Tubes (worldradiohistory.com)

This site has THE HISTORY  RADIO and BROADCAST HISTORY library with thousands of books and magazines (worldradiohistory.com) and this site is an amazing resource.  Its takes some time to figure out how to use the many search features, but once you do, it can answer many of the  questions or technically guide conversations associated with this  technology that is proving to still be relevant as it enters its 2nd century.