I agree with JIMNLIN, your 1500HD is the same frame and running gear as the 2500s of the same timeframe. As I recall, certain cab styles were badged 1500HD and other cab styles were badged as 2500. If the rear GAWR is 6084 lbs, then that is the same rating as currently used on swr 2500HD models. If you weigh the truck and compare to the posted GVWR, you can determine what your available payload is before exceeding GVWR. And if you weigh the rear axle separately, you can compare that to the rear GAWR to really see the absolute max. king pin weight. But one warning, you can't use the trailer manufacturer's DRY pin weight when looking at fifth wheels, you will have to estimate what the loaded pin weight will be for any potential trailer.
You stated that towing capacity is 7500 lbs. which is a different issue than payload or carrying capacity discussed above. Anyway, 7500 lbs seems like a pretty low number. I owned a 2000 model year true 1500 series truck with the 5.3L motor and it had a towing capacity of around 8200 lbs. But my point is that if your towing capacity is really that low, it is almost certainly due to the axle ratio and you probably have a 3.42 ratio. If the truck is 2wd, then for about $500 you can get the axle gears changed to a 3.73 or 4.10 ratio. While this won't change your "official" tow rating, it will make the truck tow just as good as any other 1500HD that came factory equipped with those ratios.