Need more information about how you were loaded, and what if any mods you've made to the truck. How much is the rear of your truck sagging when hitched? As mentioned, given the posted weights for that 5er you're probably overloading the truck, which can make it ride rough.
It sounds like you are already aware that towing the 5er nose high can exacerbate chucking. Slop in hitches can also cause issues, but in your case that probably isn't the issue given the ball mount setup you're using tends to provide a smooth tight hookup. On the downside, your hitch is probably carries the weight relatively far back in your bed, which combined with overloading the rear end might make things a little rougher.
I'd weigh the setup, and measure and post just how high you are in the front and see if that doesn't help in getting anything more than a wild guess.