Yes, i'm towing a 7x16 enclosed. 7000 lbs is very comfortable for this truck. Only on steeper grades will it drop from 10th to 9th with cruise set at 65-70. Good news is the tow/haul mode is very well tuned so it will hold 9th for duration of the hill and prevent gear hunting like the gassers tend to do. Furthermore, 10th and 9th are such a close gear ratio that you won't even notice it if you are looking for it. I can't speak for 9000+ towing but unless you regularly tow in very hilly terrain, there's ample low end torque, smooth, smart and quite transmission works with it flawlessly.
PS - anyone not sold on 3.0 vs 5.3 gas, wait until you go down a steep hill in tow/haul mode and listen to the turbo spool as it's vanes close to create back pressure. Truck will automatically down shift and turbo works to slow the truck down saving your breaks. Might not mean much to you but it does to me:)