My 2004.5 has the same running gear as you except 10 less ft-lbs. I tow 10k pounds and find that I wouldn't like to go higher. My engine is relatively stock and everywhere I go involves grades. It will do the job but My EGTs limit me before lack of power. I have heard that some tuners may actually reduce power in certain situations such as towing, but just here-say. I have almost exactly the same miles as you. Be a shame to have to upgrade that truck.
I have an Edge CTS and it does read transmission temperature off the OBD port. The readings fluctuate as would expect relative to driving conditions. The idea that the numbers are made up seems silly.