If you aren't happy with the way the 6.2 pulls, I don't think you will be happy with a 6.0, as it has less HP and torque.
I switched from an 03 2500 8.1 Burb to a 11 Yukon Denali XL with the 6.2 and 6 speed. The Burb did feel more stable towing, but the Yukon seems to have quite a bit more power. I am towing a 6500 - 7000 pound boat (more weight, less wind resistance than you are talking about) at higher elevation, and the engine/tranny work just fine.
It could be possible you got a used vehicle that has some issues. There are not going to be a lot of more powerful, 3 row options in your price range.
