Having trouble reducing the vibrations on my turntable setup

The rationale for using only three footers under any single piece of gear is that three points define a plane. Whereas when you add a fourth point you don’t necessarily have a plane. Hence the device can rock back-and-forth on any two of its 4 points. Or, one of 4 is not bearing its share of the mass which shifts a greater than average burden to another bearing. I agree that mounting a 100 pound turntable on three points is a bit scary, but it does give confidence that the turntable is nesting on a plane. After that it’s relatively easy to level the device by adjusting the height of one footer. 

I highly recommend (via my own experience) the Symposium Acoustics products.  They make a platform specific for turntables and to solve the very problem that you describe.  It's called the Segue ISO.  There are several standard sizes to choose from and also they can be made to order in a specific size of your choosing.  There are springs on the underside of the platform and you can choose to have the correct springs for the weight of your turntable.  The platform performs at it's best when combined with Symposium Acoustics Rollerblock products.  Those would be in place of your spiked feet.  Contact the company and speak with Peter (company president/owner).  He is extremely knowledgeable and helpful and will steer you properly.  The products are fairly priced and deliver an outstanding performance value.
Symposium Acoustics: (symposiumusa.com)
Best to you on your quest.

I would make sure that your tonearm and table are properly grounded and that you put it on an isolated wood stand with soft feet .

I agree, the best solution is wall mount for your turntable, but my son feared drilling anchors into his rental apartment wall. We got a set of sorbothane isolation turntable feet here,  Turntable Phonograph Vinyl Record Player lsolation Feet – Mnpctech  

Several "solutions have been mentioned which are really not.
Mass will not isolate a turntable from anything. It will just lower the frequency it bounces at. A massive table on a bad floor will skip just as much, sometimes worse than a light one. Concrete floors will protect you from foot fall problems but not from "house rumble." Even on a concrete floor you can feel the cement truck trundle down the street. Wall shelves might protect you from foot fall problems but they will make a lot of other problems worse. Walls vibrate like crazy and pass it right on to the turntable. Just play and song with strong bass and put your hand on the wall. Many have wound up with feedback problems. The only sure fire solution is a properly isolated turntable with a suspension tuned below 3 Hz. I would never consider a turntable without a proper suspension. If you really love the turntable you can always put a MinusK suspension under it. Sonically you can not do better. It is not the most user friendly solution.
With turntables like the Sota the suspension is internal floating a sub chassis. You can rest your hand on the plinth no problem. With tables like the SME and one sitting on a MinusK platform if you put your hand down on the plinth the whole thing starts bouncing. The SME is at least well damped. The Dohmann has an internal MinusK system and is bouncy but for certain is one of the very best sounding turntables made and the only one at this time I would opt for over the Sota if I could afford it.