Turntable on suspended floor - shelf or braces?

Ablang.....yes - very effective.

Not sure is this is relevant, but I bought an older but clean Linn table a few years back and stuck on top of my rack where it was NOT happy...then (of course) read the "official" manual which suggested a lower firm table and it's worked perfectly since. Low mass, level, sturdy table...done. Got lucky I suppose.

Sounds like you have the right idea and bolstering up the floor in your case by jacking it up from beneath would be easy to do.
I think a wall shelf would be best unless you have cabinets or something else on that wall that would themselves cause vibrations when accessed. But jacking up the floor beneath that wall will make that wall even more stable. And if you decided against a wall shelf a platform/table close to the wall also minimizes foot induced vibration.
Rega recommends against heavy dense platforms for their turntable design to sit on. I asked about making my own concrete slab for stability and they discouraged that method, saying that it tends to store and then amplify energy/vibrations. Suggesting instead a lighter thinner surface much like the Rega shelves. One that in their words dissipates the energy instead, much like their lightweight turntable designs are intended to do.