I think you have the V6 sizes mixed up.. ;) The 3.7 is the NA base engine. The 3.5 is the one with the twin turbos on it.. :)
I'm towing a #5000 loaded TT (including a full tank of fresh water :) ) with my Ecoboost, but I used to tow it with a 97 F150 with a 5.4 V8 in it and it didn't have as much HP as the 3.7 V6.. It had more torque, and that will get you moving easier, but you should be okay for the most part.. Just don't be affraid to rev that V6 when going up the grades..
Good luck!
Mitch