Your probably using "shipping wieght" incorrectly. Who knows what is included and not included in that number, I certanily don't.
To know your real world TT maximum capacity you need to do a couple of things:
1.) Load your truck with full fuel, all passengers, and expected gear to be carried. Go to CAT scale and get front and rear axle wieghts
2.) Subtract truck total wieght from GVWR that is your GVWR payload limit
3.) Subtract your rear axle wieght from the RAWR that is rear axle wieght limit
4.) Check your reciever hitch limits
Your real world maximum payload is the smallest of the 3 above if you believe in GVWR limits
Your real world maximum towing limit is your actual truck wieght minus the GCWR
Now your real world maximum TT the most limiting between hitch payload and towing limit. For anything other than a FW and Dually it will be hitch payload.