Best Equipment Stand

Possibly the springy Gyrodeck suspension and your self-described springy floor are not made for each other.  In addition, no disrespect to the Mitchell, but your system is worthy of a turntable upgrade. You might consider the purchase of an unsuspended turntable which you can then pair with a high quality isolation shelf, like a Vibraplane or Minus K. (You don't want to pair a suspended tt with a second suspension.)  This is worth considering if wall mounting is impractical.  Remember too that wall mounting is not a panacea; strong structural vibrations will be transmitted into a wall mount, too. You might ask an architect to recommend a suitable wall in your home that is relatively isolated from structure-borne forces. In addition, FWIW, I have had good luck with Adona rack systems.  At least they used to be reasonable in cost for very high quality; I don't know where they fit in the cost continuum as of today.  Adding the mass of a heavy rack might help with your footfall problem, or it might not.

Tom, you mention the need to level.  I can understand that for your turntable, but remember that a three legged rack, such as the Star Sound Apprentice is alway with all three feet in contact. Of course the design of all the Star Sound devices is to get the vibration to the floor and to the Earth. They would not be good for foot falls. 

The old Stillpoints component stands and pipes can be used as a two level  rack that is fairly cheap using Ultra Minis. Stillpoint technology is somewhat helpful for footfalls. You would not want to go over two shelfs high, however. 

One thing that I would discourage is wooden shelving. It robs the music even worse than rubber. There always is wall shelving but I've never had any. Vibrations have such substantial impact on fidelity that you really need to consider them.

There has to be some mechanism for dealing with seismic type vibration. Even the strongest most inflexible design rack will simply transfer the structural vibration very efficiently. In the worst case the rack will amplify the problem. I can appreciate the desire to organize and showcase the system but for the best sound in most cases the components should be placed directly in the floor using, at a minimum, some sort of footers or at best a mass on spring device(s).

I had the same problem with two turntables (Linn LP12 and a nice Rega) in my upstairs room with the hardwood floor. Tried several different racks, still could hear footfalls and the arm would actually jump around on the LP if you trod heavily into the room. So I had to move my system downstairs to my ground floor/basement level big room with concrete slab covered by wall to wall carpeting. Turntable dead silent now even if I "dance" to the music. I really think you will have to use the wall shelf to isolate your TT from the springy floor. Or pour a concrete slab?