6200lbs RAWR sounds a bit low for a 3500 SRW. That's a 2500 RAWR, traditionally limited by the LT245/75R16 LRE tires they came with. You sure about that?
Typically they run in the 7000-7200lbs range.
When it comes to hauling TC's, where there's a will there's a way. It's very easy to justify exceeding the factory GVWR when properly motivated. The first and most common method is to ignore GVWR and go with the axle ratings. That generally gives you yet another 1000lbs of capacity over the GVWR because the empty weight on the rear axle is generally around 2800-3100lbs for most SRW pickups.
It is generally accepted that as long as you're not exceeding the tire ratings, you are okay. Add airbags and/or helper springs to level the load, and go.
Why the tire ratings? Because those are the only individual components in the truck that are marked with a weight rating.