It didn't take long for me to question the shift points when my mileage towing an 8.5x20 car hauler I called the parachute. 6.5 mpg. Switched to manual and gained 1 mpg. Whooptydoo.
My 5.0 does this exact thing while towing a 600lb enclosed cargo trailer.
I tend to get better MPG in tow/haul than eco but intermittently I will be in stop and go traffic, where the transmission won’t upshift until it hits the redline and usually I’ll back off the throttle beforehand to try and force an upshift and it’s annoying as hell.
Tow haul mode is designed to minimize heat buildup in the ATF when towing a heavy load. With my GM 2500 diesel truck it was recommended when the truck and tow load exceeded 80% of the GCWR or more than 12,000 lbs trailer load.
With a 5,000 lb trailer there is no need to use Tow Haul mode which only keeps the torque converter clutch engaged longer and changes shift points. You can watch the ATF temperature to verify. Flash point for ATF is usually more than 370 F degrees.