Hummmmmmm.
Interesting problem you are having. My first question is, which radiator do you have? I know most of them by that age went to the 34" wide radiator, but there are 2 and 3 row cores. I would make sure you have the 3 row. Also, if your truck has the transmission cooler routed through the radiator itself, I would ditch that and keep it standalone. Your transmission will run hotter than your engine to begin with, so it can contribute to that. It's likely the largest contributor to your rising heat, is the auto transmission. Also keep in mind your stock thermostat is a 195.
Now, I probably have about the most similar comparison you will find. I'm not lifted, but I have a 98 K3500 454 truck, although mine is a NV4500. It has a GMC grille, but I have a 32" LED light bar behind the grille so it's about the same as your chevy grille. I have a diesel bumper but there are fog lights in it so it's null. I have the 3 row radiator with internal oil cooler. 4.10 gears and 33" tires.
This is my old camper, and the heaviest I towed. Went from western WA to eastern ID over 3 mountain passes, in 80-112 heat with no problems, truck never went over 200-210 or so while running AC. This setup was about 18k gross.
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Since then, i've made a few changes, most notably a different camper, a cargo trailer and a whipple supercharger. This setup is about 15k
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With the whipple I'm running a 180 thermostat, and climbing long hills because of the boost and being non-intercooled it moves up to the 210ish mark, but that is about it.