Fundamentally, if the transmission is changing gears or unlocking/locking the torque converter more than every 5 minutes, then limit the top gear to one lower. So if you are hunting between 4-5, then just stay in 4th. That 6.0L will last for 300k miles at 3000rpm under load. You will get better throttle response and probably better fuel economy in addition to reducing transmission wear.
Are you using the transmission's Tow/haul mode? If not, please do. GM also has the "M" mode which is really just a top gear range limiter vs. a manual mode. When I tow my TT, I use T/H plus M4 or M5 depending on the conditions. And like yours and your family, everyone else is happy watching movies, electronic devices, car games, etc and sometimes forget we are towing.
All 2008-2013 3/4 ton GM SUVS have 6.0L/6-spd/3.73. 65mph in 5th gear is about 2200rpm and 4th gear is 2800rpm. I tow at 65-72mph in 5th or 4th. My wife usually doesn't complain until the tachometer is over 4500rm, and my shoulder sometimes hurts if it hits 5500rpm. The truck is fine.