Kenneth, my first thoughts, too, were of casters, but this may cause a height issue for you, and the farther apart the casters - the beefier the "dance disc" would need to be.
What about a layer of marbles, lots & lots of marbles, poured loose under a 3/4" T&G disc, with a little baby powder thrown in for sound deadening & lubrication? This would keep the height much nearer to the rest of the stage, and only need be held in by a retaining lip surrounding the disc.
I don't think you'd have to fill the entire area, but probably about 3/4ths of it would give you sufficient roller surface & equal support.
Plain, basic marbles used to be readily available in bags of 100 or so, and quite cheap.
I'm intrigued with the idea; perhaps Henry will give his take on this, too, and we'll see if I'm "off my rocker" (or lazy susan, as the case may be.) Good luck!