Reddit mentions of Rug Wrench Washable Non Slip Rug Pad - Protect Floors While Securing Rug and Making Vacuuming Easier

You don't need a particular DDR mat. Get a rubber mat, like the one people put under rugs. It will be virtually impossible for your ddr pad to slip on this.

Random 1st thing that popped up on amazon: http://www.amazon.com/Rug-Wrench-Washable-Non-Slip/dp/B00SPIZG7G/ref=sr_1_7?s=furniture&ie=UTF8&qid=1456890557&sr=1-7&keywords=rug+pad

I've never leveled a table but that sounds annoying at best.

If it were me, I'd get a much bigger rug and cut the thing so that the feet make direct contact with the floor and so that I could remove it entirely for cleaning, or whatever. I just made this drawing. The peach is the carpet, and the black line is the slit I'm talking about, with circles cut out for the feet. If you get a good rug pad it should stay in place where you make the slit on the side..

That is what I'd do :)

EDIT: Note about the rug pad, I'd cut it the same way as the rug, but I'd install it so that the slit in the rug pad but installed 180 degrees opposite. This way the slit in the rug would be on the solid side of the pad, and the slit in the pad would be on the solid side of the rug.

EDIT 2: You could also use a flexible glue and something very thin (like fabric) under the carpet so that the slit wouldn't come apart.