Assuming 13,500 lbs loaded, and I think you will be at least at 22% pin weight, you're looking at 2970 (Probably 3000 lbs).
In my particular example, I loaded my 5er with 1140lbs of "stuff" and my pin weight increased by about 440lbs. Result increased my pin weight percentage from 20% dry to 22% loaded. So, 38% of my weight I added to the 5er from dry to ready to camp went on my pin.
If your cargo capacity is 3100, you will no doubt exceed that, by a significant margin is my bet. Assuming at a minimum you and one other passenger, you're probably talking 350 lbs of "people". Add 250 or so for hitch (maybe only 60 lbs if you go Andersen), then you're looking at weight of 3600 lbs against a cargo capacity of 3100lbs for the truck.
Doesn't even address the RAWR. If you don't know your current axle weight, you can get an estimate by looking at the curb weight specs for your truck. Add about 3400 to that weight (3000 pin weight and 300 lbs hitch weight), and if that total is less than your GRAWR, then at least you are okay there.
You should know that in almost every instance, just because a manufacturer says you can pull something that weights 14200, that you will, in all likelihood, exceed individual ratings BEFORE you reach that number.
I wish you luck...Glad you have access to scales. Think you will be shocked and disappointed. Hopefully not.
Hope you'll come back and tell us what the "rest of the story" ends up being.
Mike