I also have puzzle mats, and I find that gliding discs do work, but they don't move as well as on carpet. Fine if the moves are used to tax the moving leg (thus providing more resistance), but not as good if it's the stationary leg that is being worked (as it puts more work on the moving leg than if the discs slid more easily).
You can get a piece of carpet remnant to use for most of the sliding moves. It looks like a 2 foot by 5 foot piece would work for most moves.