I dont have a lot of experience with the 6.0, the rumblings I have heard is that it didnt like the power adders.
Have you had the truck specifically checked out by someone familiar with this engine ? I would be curious what an evaluation of the injectors and fuel system would yield. It almost sounds like you have a restriction somewhere, was the truck always like this ? I would avoid a power adders until I was sure that the truck was running right.
My 05 Chevy gets about 11-11 1/4 on summer fuel and will only come out of OD a few times between home and Florida. In the winter my mileage will drop to about 10 until I get south of Cincinatti and the amount of kerosene in the fuel goes down. I always tow in tow/haul mode and typically run between 60-65 MPH. My trailer weighs a little under 9K fully loaded.
The biggest single improvement I made was the 4" turbo back exhaust. The 05 LLY series Duramax runs hot, I have made several modifications to the truck to help it shed heat but the exhaust was the most effective. I do run a towing programmer and that also helped with the mileage.
My best advice would be to find seek out someone with 6.0 experience and pick their brain for possible solutions. An online forum may be helpful also but dont put too much on what is said there until you can sort out the personalities a little.
Good luck