Turntable Causes Speaker Cones To Excessively Move Rapidly

No, is a solid concrete foundation 

Also, I get psychosomatic about my speakers. Could I have damage them already? What damage would I look for? Sometimes it feels like the base isn't as tight as it was before. But it could be in my head because I get pretty fanatical about damaging my speakers. 

Lower the arm on a record that is not moving and tap the rack that the table is sitting on. Do you hear the tapping? Since you have no problem when streaming I doubt that you damaged your speakers!

Super unlikely you damaged your speakers. 
rumbling is caused by many things  including cartridge alignment issues, mismatch between cartridge/turntable/phono stage. 
you should post pictures of your system as it would be easier to rule out component placement issues. 

If you are determined to make things work with analog you need to have your cartridge alignment checked including VTF. Last thread you posted you were asking if you need stylus force gauge.
How do you know it’s not the VTF that’s causing the rumble.

Have you verified your cartridge is set up correctly? Did you get a stylus force gauge? This one on amazon will do the trick. I use it and like it a lot 

https://a.co/d/0is3Y04w