What you need is to keep the speakers from moving in the direction of what the drivers are moving, so that the drivers can push air without the cabinet fighting it. I believe the ADS are front firing drivers, which means you need to keep the cabinets to be kept still in the fore-aft direction, mainly. Of course it's better to eliminate motion in all directions.
As for carpet below the stands, its best to increase mass at the base of the stands, and use something with spikes (below the stand) that penetrate the carpet and padding to mechanically couple the stand directly to the floor (wood or concrete). This hopefully eliminates the carpet/pad spring that otherwise allows the speaker to bounce or rock.
After that, you can consider stiffening the stands so it doesn't bend.
As for carpet below the stands, its best to increase mass at the base of the stands, and use something with spikes (below the stand) that penetrate the carpet and padding to mechanically couple the stand directly to the floor (wood or concrete). This hopefully eliminates the carpet/pad spring that otherwise allows the speaker to bounce or rock.
After that, you can consider stiffening the stands so it doesn't bend.