No way you have 2000 pounds of payload. That's more likely 1400-1500 pounds. Some of the 8.1L 3/4 tons don't have 2000 pounds.
That TT would put your vehicle over at least 4 of its ratings and quite frankly not be comfortable for anyone. You could spend $2500 on a premium WDH plus another $2500 on suspension upgrades and you'll need a replacement receiver if it is still the stock round tube design. And even with those mods, you are still over the truck's ratings and I'm not sure it would be comfortable. Then you have a performance issue with the 5.3L/4-spd trans. That's solidly into 3/4 ton range, and if you are looking at similar era of early to mid 2000s, you will want the optional engines. So 8.1L or diesel for GM, V10 or diesel for Ford.
A & A parents of DD 2005, DS1 2007, DS2 2009
2011 Suburban 2500 6.0L 3.73 pulling 2011 Heartland North Trail 28BRS
2017 Subaru Outback 3.6R
2x 2023 Chevrolet Bolt EUV (Gray and Black Twins)