I wouldn't and I'm far from a registered weight police guy. Heck I tow 200lbs over my GVW right now. My thinking is that I've BTDT. Towed 7300lbs @31' with an F150. with maxtow. Forget about the doggy 5.4 it had, it was the overall handling that I didn't like. 70% of the time it was just okay. The rest while not white knuckle was attention grabbing.
6900lbs will be 7900lbs if you have kids. 12% of 7900lbs is 940lbs. That leaves you with 464lbs for family. I'm guessing that's close to what yours is. Now couple a maxed out truck towing almost 34' @7900-8000lbs and IMO it's white knuckle time. You won't like it unless you're just going 50-60 miles for a weekend trip. Then I guess you'd just get used to it. But like mentioned before if you're planning on seeing a larger area then 5-7 hrs of pulling a 34' 8000lb TT with a maxed out truck and a couple kids wanting to know if they're there yet could be unnerving IMO.