The body and everything inside the cabin of the 3/4 ton Suburbans are the same as the half tons. The frame, axles, springs, wheels, engine, trans, shocks and some other components are different. Visually, they are difficult to tell apart except the relatively ugly 8-lug wheels and side by side the half ton is about 2" shorter in height.
Here is an example.
Ours is a fairly well equipped LT with 2051 pounds of payload of comparison to yours. I can tow our TT to/from storage without WD compared to our prior half ton requiring it, although we only have 750-800 pounds of TW.
I think you are likely right at GVWR and rear axle, and over tow rating/GCWR assuming you have the 6-spd trans, 3.42 axle and HD towing package. I expect a very noticeable increase in stability with any late model 3/4 ton pickup, as well as if you can find a 3/4 ton Suburban or Yukon XL. I recommend 2008-2013 for the SUVs, or 2011+ for GM HD pickups.