I own a 35 foot Keystone Bullet pull behind and pull it with a Yukon XL Denali. Dry weight is a few hundred lbs less (6100) than the OPs. I have since upgraded the hitch to a Hensley Arrow as the Blue Ox Sway pro WDH wasn't effective in 30 mph winds. That paired with a good brake controller, LT tires, premium brakes/rotors, and loading everything in the trailer except for humans and car seats has made for pleasant towing trips. Grant it, I am pretty close to payload capacity on the Yukon, but not over. After a couple more RVing seasons, the kids will be bigger and we will upgrade to a 3/4 ton truck. I'm all about staying within the numbers. But these half ton trucks are capable tow vehicles as long as you stay with the specs. Pack lite, keep your water tanks empty, and load the trailer equally on both sides of the axles. The Hensley completely eliminated sway after I purchased it last year, something I highly recommend for a trailer over 26 feet in lenght. A 3000 mile trip to Disney's Fort Wilderness proved its worth after a roadway hazard almost took out my rig at highway speeds. The evasive maneuver I executed to avoid the hazard would have been catastrophic with anything other than a Hensley.
Personally, I would only look at long wheelbase SUVS (Suburban's, Yukon XLs, and Expy's). Your WDH should be nothing less than a midrange hitch (Equal-i-zer or equivalent). And keep an eye on capacities. If you exceed them, you need to move up to a 3/4 ton vehicle. And most importantly, drive like an old man. Speed kills, especially when pulling 7,000 lbs.
Good luck on your TV search and safe travels.
