Tahoe is in the mountains, right? That's why the poor mileage. I average about 8.5 mpg in my 2005 (four speed auto, 5.4L) with tow package. It would be better with more speeds like yours, but not so sure it would affect gas mileage that much. I have to run in the 60-63 mph range to get mileage like that. Drops at least 0.5 mpg just going up to 65! I'm pulling a 6000# 30' V-Lite trailer though, so I'm maxed out since tow capacity is 8200#. Only a few hills between Lexington SC and the Myrtle Beach vicinity -- the only place I've pulled this combo so far. I expect to drop speed to about 45-50 mph pulling hills in the SC/NC mountains, and lose at least 1 mpg even doing that. I was pulling a 5000# trailer with my 2003 Toyota Tundra (4.7L, four speed auto, 7200# rating) and did about the same. With the bigger motor and heavier trailer it should perform on a par. Got the Expy so I'd have a little more "umph" to pull the 6K trailer, only to have wife see the new trailer and "had to have it", so now max the Expy out!! Oh well...
The only mod I made to mine is adding a big sway bar to the rear to reduce rear end "wallowing". Made a huge difference over that scrawny stock bar! IIRC it's a 1.5" bar... If you're concerned about the trans temp get a bigger cooler. Stock tow package comes with a modest external (not inside the radiator tank) cooler that should be big enough though. Looks like you're mostly staying under 220 degrees, which is good. Won't hurt to hit 220-240 ON OCCASION, like when pulling a hill, but it should cool back down to under 220 shortly after hill has been breached. Here's a good article on trans fluid temps:
https://www.transmissionrepaircostguide.com/transmission-overheating/
Your hitch looks like it's adjustable. I don't think bringing the hitch up one position will affect mileage, but it will level out the trailer and should make it tow a bit better.
