Usually the dually rear axle is rated for 8,000 lbs. or more as with these trucks the weakest link is the tires and adding 2 more nearly doubles the load capacity. Subtracting the weight of the truck at the drive axles gives an approximate maximum payload.
The problem with the payload ratings is that if you have a crew cab the manufacturer down rates the load to allow 150 lbs. per passenger seat or 750 lbs. with the crew cab configuration.
The rear axle and wheel bearings are rated for at least 8900 lbs. so the weakest link is first the tires and after that the leaf springs followed by the strength of the frame.
There is something else wrong with your numbers. I have a SRW 2500HD that has a payload rating from the factory that is greater than the 2482 pounds mentioned. It is actually less than the payload rating of the new Ford F-150 trucks with 17" wheels.
When I was looking at new trucks on dealers' lots there were always similar trucks with very different payload ratings and the difference was usually with the rims and tires on the two trucks.
Trucks can come with different axles depending upon options and whether the engine is gas or diesel and with different leaf packs and with different rims and tires. All of these factors affect the calculated value that is put on the sticker. Most of these factors are easily corrected by the owner to improve load capacity and handling.