Don't worry - you'll do just fine. Last fall I pulled my loaded Passport (6950# CAT scale weight) through the mountains of northern Vermont and New Hampshire via interstate roads without any issue. My 3.6L V6 GMC Canyon did not over heat, did not hunt gears, and passed semi's going uphill and downhill. I did not have any problem maintaining 65-70 MPH uphill using cruise control.
Be sure that the TV is in TowHaul mode EACH TIME YOU STARTUP the engine and use cruise control when driving interstate roads. The TowHaul/cruise control combination will tell your computer to not shift the transmission into high range and will avoid/delay gear hunting for power.
Keep in mind that the V6 gets its power from high RPM so you will be close to redline when going upgrade. If you're TT load is within the TV specs that high RPM will not hurt the engine or transmission and will not cause your radiator or transmission to overheat under normal conditions. That high RPM, however, will require more fuel - I got only 9.5 mpg through those mountains so plan on more frequent fuel stops.