Another option would be Onion Valley to Whitney Portal via Mt. Whitney. This way you could still climb Mt. Whitney, and enjoy better scenery, better camping sites, etc.... Check out:
http://www.whitneyzone.com/wz/ubbthreads.php/topics/25745/Onion_Valley_Whitney_Portal_Ju#Post25745. This trip report has lots of pictures, and suggestions about camping spots. It would take 4 days I guess, and you would need to hitch a ride from the Portal back to your car, or from the Portal (where you leave your car) to the trail head.
I'm not sure of the details of the permits, but this would give you a different option. I understand that you do need an exit permit, but I have not idea how difficult they are to obtain.