In 1984 I soloed the gullies in six hours from cabin-to-cabin. I went up North, down Damnation, up Yale, down Diagonal, up Pinnacle, down Central, up O'dells, and then down South. The weather was so bad, 35 degrees with fog, wind, and blowing snow, that I didn't even see others appearing in the ravine until I was halfway through, even though the cabin had been full the prior night. Probably not the wisest time to go or the best descisions on which routes to downclimb, but it just felt right as I did it. Besides, I had just ended a relationship (OK, she ended it...) and being young I was in that "don't give a damn" frame of mind. That definately helped in Chamonix, too.
Definately give it a go, it was an incredible feeling of accomplishment. These Old White's really are a great training ground for just about anything.
Good luck, let me know how you make out!