I hate the weight police, but this trailer dry (meaning no propane, no battery, no food, no clothing, no dishes, no beer) leaves the factory just shy of 6300 lbs.
Start tacking on "stuff" and you're going to be well over the towing capacity of your truck.
I tow with an Expedition and a 9300# tow rating and can definitely tell the Cherokee is back there.
As far as the Tow/Haul button - I use it every time, RPMs race and performance really suffers when I don't.
Craig & Lynn D'Angelo