On most pickups, it is the stock tires that limit the RAWR. Replacing the stock tires with higher load capacity tires will "unofficially" increase your indicated RAWR. Notice that your RAWR is suspiciously matched to the load capacity of your stock tires. Replace the tires with larger load range E tires with higher load capacity and you have effectively increased your RAWR. The axles themselves in these trucks are rated for well over 10,000 lbs, so that's not the issue.
The issue becomes that you will be slightly over the truck's GVWR (which was determined using the stock tires as well). If you're OK with that, and still have a rear axle weight under your tires' weight capacities when loaded with pin weight, then you shouldn't have a problem.
We have a 2005 Duramax, 6084 RAWR with the stock tires, but we have 285's with 3750 lbs capacity each, giving us an effective 7500 RAWR. We're nowhere close to that when loaded, but are still over slightly on our truck's GVWR, and have been towing our 12,000 lb loaded 36' three slide, 2 bedroom, loft unit for 4 years with great handling and no issues. Hope this helps.
