The crew cab Silverados with the 5.3L engine and 3.42 rear axle tows 9600lbs when equipped with the heavy duty trailering package.
The Voretc Max gives you 10700 lbs max towing.
Is there a particular reason you absolutely need 3.73 rear axle?
My 2008 Silverado had a 3.73 rear axle, but it only had the 4 speed automatic.
IMO, if I were going to tow more than 9000lbs on a regular basis, I would get a 2500HD, maybe with a Duramax.