Not sure if this will help but I used to tow my WW toy hauler, 12,000 lbs loaded, with my Chevy 2500HD. It had the 6.0L motor and a Whipple supercharger, air bags in the rear 35 inch tires and 4.56's. It towed it very well, only time it wanted to overheat was when I fought a big head wind and really had to push for long periods of time. Other than that it towed very well. Just watch for when the tranny starts to slip the torque converter, all that power and the tranny slipping can heat the tranny really fast. I would just get out of it a little until the torque converter would lock up again and then it was fine. I had the 4L85E not sure if the H2 has the same or the 4L60?
Hope this helps,
Chris