Kinda off topic,but try it with A WDH installed.
Weight wise ,your setup and mine are very similar.I have an 06 F250 towing a 2008 cherokee bunk house thats close to the same weight that you are towing.
I've tried my both ways.My truck handles the trailer fine without any Weight Dist. Out of Curiosity I spent a couple hours one evening setting my hitch up.
the hitch when setup took a good towing setup and made it excellent.
Short answer ,,truck and trailer tows like its one solid unit and basically only thing you feel is the added weight.
No sway,no rear bounce on rough spots in road,etc