should I suspend a floor-standing turntable?

There is no real solution to your problem. Soft things like wood, rubber, etc. will just rob you of dynamics. About the only thing that is realistic, I think, is a three inch thick piece of granite, not marble which just rings like a bell. Place the granite into a larger wooden box that is partially full of sand. This will dampen the ringing of the granite. My wooden box had a sheet metal bottom and had no projecting screw heads or feet, which would ruin what you were seeking. Mass and the irregularities of sand were where you were placing your bet.

This does nothing for springy floors. Nothing other than an adjustable pole placed under your floor and run up tight against the floor from below. I doubt if you can do this. Wall mounting is no real solution as the walls vibrate also. Perhaps using the rafters above might be useful, but I've never tried that.

Stringreen, this certainly has not been my experience and neither is hanging from the ceiling. In one home I had earth below where the turntable was and used a three inch pipe with a screwable plate that really did help and in another house built on a slab putting the turntable on the floor was quite good. Elsewhere sheer mass was the answer. I once heard a system in Chicago where the guy got curbstones under his turntable. Each weighed about three hundred pounds.

Schubert, I can see where that would make a big difference. Where do they run piping and wiring? Or is it just plastering over the walling?

Schubert, yeah, here expensive houses have nine foot ceilings rather than eight foot ceilings, and really expensive houses have eleven or even fifteen foot ceilings. But all are drywalling, usually using eight foot tall pieces. But we had friends with an old house where the wall were just laths with heavy wall paper glued to them. You could see them move when the wind blew. I guess it must have been like heating a tent in the winter.