I have the very same truck with 97000 miles, same rearend ratio. I have towed 2 dikfferent TT with this truck however the longest was 24ft.
You are really pushing thelimit with the length of your current TT. I would say your only hope is a Hensley type hitch. I've always used Equalizer type hitches with shorter TT. The other main problem you have is that you have too much TT for the truck. I would not consider any weight load over a loaded 6000 lbs for my truck and then it really struggles in the hills of Colorado. That's one reason I have the TC I now have.