Glad to see your truck isn't any heavier. My 2001 Dodge Ram V8-318 was at 5,218-lbs "empty" (driver + full fuel). 12-mpg isn't bad in consideration, it's better than what some report for towing. That truck of mine had neither decent mpg nor towing power which is why it was traded for what I have now.
The tweaks I mentioned have to do with setting up the weight-distribution hitch according to certified scale readings. The adjustments to bring the combination to "fingertip control" in all situations may take several tries. But the reduction in steering and braking applications per 100 miles will drop dramatically (noted by Kenworth and Cummins as central to improving big truck FE). It will also help in dialing in the best tire pressures across the rig, and make any readings of temps or pressures otherwise as low as possible (to complement or make clear of error your other FE changes).
Travel trailer axle alignment, a set of shock absorbers & balancers, plus the elimination of brake drag on both vehicles (and on the truck: any -- even minute -- steering gear-induced "wander") are the balance.
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