As with any 1/2 ton rated pickup (for the most part) you will run out of payload well before towing capacity. There are things you can do to help out with payload like air bags or super springs but I would be cautious. What is most important is the safety of you, your family and anyone else that might happen to be traveling near you when you are on the road.
It looks like your TT GVWR is 6600lbs from what you mentioned (Dry + CCC). If you were fully loaded then you would be close to the GCWR for the TV. No doubt the F150 you mentioned will pull a 6600lb trailer. It's doing it safely, in control and being able to stop.
RAPTOR 300MP
RAM 3500 MEGA CTD 4X4