Man, you can tell its winter. Folks are fixing stuff up inside!

My ol' house is 100 plus years. Living room is just short of a trampoline and I've played with it for years for less bounce to the ounce, but not done all that well with the old joists sometimes being split.
For examples: I had my gear across one outside wall (above the brick foundation) but still couldn't play vinyl without going nuts anytime anyone moved in the room. Put a 4x4 across the bottom of the joists with 2-3 steel support columns under it (with concrete floor there), but it was not all 'that' for fixing it. I put 1-2 2x6 on every floor joist, completely across, nailed every 12 inches. It was some better, but still, no joy.
The ONLY way I got the turnatble stable was directly in corner of the room, where there were supports under both walls. I considred a wall mounted stand, but didn't want to mess up my plaster or face another failure after I had spent the money for corner-shelf.
Eventually, I moved it to a system in newer part of the house.
I live with the spring that is left, tired of it rubbing my nose in what I couldn't fix. It works good enough for cd and squeezebox listening.
I also considred 'loading' the floor with a buttload of weight so it would have a downward sway that merely walking across the floor wouldn't budge. Again, easier to move...

Hopefully, the method Charlie described will do you for less-than 'turntable bounce'.
Good luck! Let us know if you have divined a more successful method!!
Regards,
DeadFish