If you want to go by the book, you can't increase the 1625lb payload. If you try anyway, make sure to look at everything (tires, rims, axles, springs, etc...) Air bags will level the load but everything else is still over capacity)
After subtracing a couple hundred lbs for the hitch and probably another few hundred for misc cargo in the truck, you are probably looking at less than 1000lbs capacity available to handle the pin weight. That would be a tiny 5th wheel. Figure around 20-25% of the 5th wheel as pin weight for a starting figure. You also have to be careful with toy haulers if you tow without the 1600lbs of motorcycle in the back as a counter weight, you might be adding 800-1000lbs to the pin weight.