I have 2 of the big mats, 36 by 24 or something like that.
One is worn out, I could use the corner for the turn table.
and a wooden cutting board, never used, (10 by 14)
I could paste a piece of the mat on that and lay it on top of a lazy susan. Worth a try anyhow.
As for cheap fabric, I seem to find lots at gr sales. Especially where the senior people live, cause they are getting rid of their stash, for whatever reason.