Why do my bass drivers shake violently listening to vinyl

+1 erik, problem most likely subsonic 5Hz or so. Use a 24dB/octave filter, the steeper the slope the better.

@lewm

I generally prefer to go from the simple to the complex, in trying to solve any problem. Simple is to either move your turntable in your listening room or suspend it, or both. Complex is to add a subsonic filter

I agree wholeheartedly with this approach

FYI: Japanese cartridge specs are rated at 100hz not 10hz. You have to multiply by 1.7 and the resonance frequency is not 11.12 it is 8.53. That is a fine figure and will not cause the problem of woofer pumping! 

"Working" from home today so I moved the TT from within the dormer area on the Pangea shelf to outside of the dormer on a much more stable IKEA Kallax shelf. (see Audionoobie's system pics) Was pic 4, now is pic 3. 

Same problem....

Seems like I'll be looking for a rumble filter.

That's very interesting.  You mentioned you are using a 1200GR turntable.  Do you own or can you borrow a different TT, just to see if the problem is the same with a different source TT?  I am wondering whether there is some sort of defect in your 1200GR.  That seems very unlikely, given that Technics make thousands of them and have vast experience building TTs with a very low error rate, but unlikely events do occur.  If you own a stethoscope, place the bell on the plinth and listen for excessive noise; that might be an indicator of a problem. (It's also interesting that a Pangea shelf is not as stable as an IKEA product not even made to support a TT.)