I towed 6,600 +/- lbs from NJ to SC & back. Used tow/haul and let the truck take care of the shifting. It stayed in 6th 99% of the time with plenty of pedal left and I got 11.5 - 12.5 mpg.

6.2L with 35" tires so your results might be alittle different but you have a lighter truck & trailer.

 

Pulled a very similar load with my 5.0 recently. Never went to sixth except on flat or downhills and speeds greater than 60mph. I locked it out after that. Of course, I lock it out when empty too when traveling under 60mph.