Before going to the 19.5s, check your weights with everything loaded. With using a weight distribution hitch, I think you will find you are running over GVWR but under GAWR. The GAWR is the most important numbers in my opinion. You will find the rear axle limited by the tires.
I run a similar setup with my 2,400# TC and pulled a 6,000# jeep/trailer setup which added 650# to the front axle. I did not run a weight distribution hitch on this setup and still was under the GAWR even with four adults in the truck and a few hundred pounds of camping gear on the floor.
But if you go to the 19.5s, you definitely won't have any issues.
However, keep in mind the big difference between towing and the TC is the Center of Gravity (COG) is higher which tends to make the vehicle sway a bit more.
May want to consider a set of stable loads which will help engage the overload springs sooner and help prevent so much squatting.