If the trans has tow/haul mode, use it. If you can limit the trans to not use 5th gear, do that. Every time the transmission shifts, the torque converter unlocks and heats up.
Change all the fluids, especially transmission fluid. Keep in mind the 9000+ tow rating is with the proper equipment, mainly differential gearing and transmission cooler. You should verify you have that equipment. Even if you do, 7300 pounds, especially dry, probably puts the Armada over the receiver rating as well as GVWR when loaded up with the family. You are pushing the limits on an 11 year old vehicle, so proper maintenance is vital to keeping that TV running and towing well.