Turntable Causes Speaker Cones To Excessively Move Rapidly

I had your exact problem with my Technics SL-1000R turntable and a Hana Unami Red MC cartridge. I also have REL Subs x 2 allthough my system is on a suspended floor. I spent every evening and weekend for a couple of weeks trying to find a solution - I ultimately gave up and bought a Burmiester 174 Turntable that fixed the problem. I can offer some tips for things that did make some progress for me. 

1. Added 7x subfloor jacks in my crawlspace (doesnt apply to your situation) 

2. Made adjustments to how the washers that hold the platter were installed and how tight the screws holding the platter were tightened. (this made a pretty big difference) 

3. Added IsoAcoutics Iso Pucks below the Subs (this was probably the biggest improvement) but it still didn't completly fix the issue

4. Added IsoAcoutics isolation platform (Didn't help much) 

5. Used a MOFI Heavyweight Record Weight (Didn't help much) 

6. Hired a "pro" from the audiophile store to come over to my house to make finite adjustments to everything (waste of money) 

7. Hired another "pro" to come over and make more assessments (didn't help much) 

Finally gave up and bought a different turntable and That Finally Fixed It! 100%

Through it all, the washers in the platter made a big difference and the Iso Pucks under the Subs were the biggest improvement but ultimately I couldn't get it figured out completely 

I did all of the modifications myself after speaking with loads of knowledgeable people. I added the Isoacoustic footers (which did little). I then installed the upgraded tonearm (which did little to help). I then added an isolation table (again didn't help). Changed phono cartridges (A Kiseki to a My Sonic Labs which didn't help). Changed dual subs (From Rel 212SX to Rel #31's which didn't help). It was only when I ordered a new main bearing for the platter and did that installation myself that I realized the motor was actually not tightened down properly. That was the problem all along. A long and expensive journey but now worth it to me in the end because I really enjoy my vinyl music. My belief is that you have something loose within your turntable creating the vibration which carries through your system to the speakers. I hope this can help you.

Took a nap, had an idea:

re-configure your equipment rack to a double wide unit, about 48" high. that is a very nice height for a TT

move the sub far right

move the light fixture to the left end of the wider rack

that moves the left speaker further away from the TT, 

Toe the speakers in, move the listening chair to the new centerline

and make a false back, dark color, to hide all those wires

https://www.audiogon.com/systems/12369

Hey, big news flash. I thought maybe it could be the rubber mat. I tried plaing a record without the rubber mat and I did not notice any woofer movement!

It is the stock rubber mat that came with the turntable. What are ya'lls thoughts about this, please?