I am just 460# shy of my GVWR of 6900# on my Tundra with 760# tongue weight. (CAT scale) This is with only me in the truck and a full tank of gas. Once I add the DW and some stuff in the back seat and the bed I will be about 200# shy of GVWR. The pin weight of a 5ver will probably put you way over your GVWR. I see a 3/4 ton truck in your future! I have essentially the same truck as you and it weighs 5700# with me (185) and a full tank of gas.
2012 Toyota Tundra 5.7 Litre DoubleCab
6 speed, 4.30 Limited Slip, Tow Package
2013 Jayco White Hawk 27DSRL
2010 Jayco JayFlight 26BH sold
Yamaha EF2000is Generators (2)
1996 Honda CB750 Nighthawk