We have show dogs.. So a truck wasn't going to work. We bought a ninth gen 1500 Suburban 4x4 for the ability to have a lot of air conditioned space. Our TT is a 27 foot Dutchman - Coleman with a slideout. The wet weight is around 6500. The Suburban does really great as it relates to the chassis and stability. The iron 5.3 does OK. Haven't had any transmission issues..yet. I do a drain and fill of the transmission fluid at every oil change and I changed the transmission filter in the spring. I custom made a drain plug so pulling it is easy and quick. The stock Chevy transmission drain plug is garbage. Personally, I would recomend a 1500 Suburban with Sumo Supersprings to help out the rear suspension. Our friends tow heavier than us with an Expedition XL and have pulled that thing over most of the US. The 5.4 makes good power for them. They haven't had any transmission repairs. Where I store my camper there's a couple that pull a bigger camper than ours with a ninth gen 1500 burb.
The Suburban gets a bad rap as if it's drivetrain is different than the Silverado/Sierras. It's the same. All the engine, transmission, differentials parts are interchangeable. Mine is a daily driver. I bought it to just use to pull the camper when I sold the motorhome. But, I liked it so much that I sold my CRV and commute with the burb. The 5.3 is a ballance between fuel economy and power. It doesn't have much in the way of low end grunt. It likes RPMs. I learned that sort of the less than easy way. I was pulling a long hill and the speed was bleeding off, I was staying off the gas and it started coughing and the check engine light came on. I figured out that it cant pull it's self and 6500 pounds of camper up a mountain at 1100 RPMs. Pull it down into 2nd and it will pull up any mountain at about 45MPH. I leave it in drive (tow/haul) out on the interstate. If the interstate turns into a lot of hills I pull it down to 3rd gear and stay around 60-65MPH just to save the downshifting. From my house to Myrtle Beach it's a flat run and it has no issues. From my house to Tennessee it's a lot of mountain pulls. It's slow in places but, I'm not in a hurry. I never floor the gas pedal. Only one time have I ever floored the burb and that was just to see what it would do. The 5.3 pulls that big sucker along in a double time hurry.