10 to 12 years ago I went from NC to FL and back a few times, towing with a 2000 Silverado 5.3L, 4 speed auto, 3:73. I got around 13 mpg, if I remember correctly. I tried to drive around 55 to 60 mph, which seem to be the mpg sweet spot on that truck. That was, before there was so much ethanol in gas. I would expect less mpg with today's fuel.
I used the tow haul button and let the tranny choose to do what it needed, using all four gears.
I drove that truck 227,000 miles. A friend of mine wanted that truck when I was ready for a new one. He is still towing his SOB with it.
2014 Silverado 1500 5.3L maximum trailering package (yes, I'm towing the 34')