i have this little bit of play as well (most notably when trackstanding) and cannot figure out what is going on. i have pulled my rear wheel as far back in the dropouts as i can but i can never pull it back far enough on both sides. the cog side is perfect but then the wheel is skewed to the side and i can't pull the other side over and keep that perfect tension at the same time. i thought about getting a tugnut but would that even help? maybe a new chain? i believe i replaced my chain a couple months ago though...hmm.

wish i could find a simple solution like you did.