When running most half-tons close to their limits, like you are, you really want to stiffen the suspension and use LT tires. At least I did and am quite happy with the results.
Despite all their advertised numbers, the suspension and tires really seem to tuned more for an empty truck. Guess that's because they run empty most of the time.
Of course, you can also buy a new HD truck that does all that for you, and gives you a higher payload, more robust drivetrain and other components as well. I may do that in a year or two, as I want a 4x4, and am 2% over my truck's rear GAWR already, and want to add even more batteries to the trailer tongue.
Good luck.