i would say keep the cat (who has to be seriously PO'd) out of the room, and/or stop using steel wool to clean the monitor.
stupid jokes aside, if they're deep scratches then forget it.
if not, you could always try doing a seies of buffing runs with a car buffer and proper materials, but in all honesty i think chances are it wouldn't come out much better, and most certainly would be more trouble then its worth.
this is a perfect case of "good reason to upgrade"
good luck.