Hey Indra! I think you will find the HD600/650 really do respond to balanced operation. Starting with the HD650 cable is a good way to proceed, so long as it is not too expensive to convert. It may be voodoo or placebo or whatever, but I always found the copper cables to sound best with the HD600, while the mixed silver/copper or silver cables were better with HD650. For HD600, I preferred the Moon Audio Blue Moon, the Cardas (like Dusty said), or the HeadRoom Fat Pipe, which was also some kind of Cardas iirc. I will look around and see if I have anything I can send your way.
@Nate: Indra says the balanced outputs are 1/4" TRS so that may require some details on implementation.
EDIT: Oh, and you can find Vicki in the thread on Bicycles and Cycling, which is where her interests lie these days.