A 1500 Z71 truck with a 1569 payload ........ may have a 6800-7000 GVWR with a 3800-4000 lb RAWR with P tires.
These small semi float GM axles don't like to be operated overloaded so stay within their door post ratings which includes tires/wheels and rear spring packs.
For a small truck like the 1500 that have small payloads I would suggest weighing the trucks front and rear axles separately. That way you know what your working numbers are especially the rear axle numbers as it can carry all of a TC weight.
I see LT tires and rear suspension help for your truck.
Now having said that if you have a '04 1500HD model then the truck has a 8600 GVWR with 6084 RAWR and E tires and wheels with up to 10xxx tow rating and up to 3000 lb payloads.
The devil is always in the details. Good luck on your search for the right TC