I've got what sounds like a similarly spec'd Ecoboost with about 100 lbs more payload than you list and a 6500 GVWR trailer. I do have the factory transmission cooler and heavier factory rear end bits. After a few trips, the longest about 2800 miles, over plains, hills, mountains, gravel roads, etc. I'm not an old hat at it by any means.
We generally travel on the lighter end of the spectrum than most people I see out. We have clothes and food for four people for a week, lawn chairs fishing poles, and not much else. We move around a lot and don't lay around the camper watching TV. We eat in it in the mornings, take showers and use the bathroom, and sleep. The rest of the day we're out doing something. No rugs, patio lights, dog kennels, freezers, satellite dishes, etc. I rarely carry much more than a few gallons in my tanks.
I've got a nice WDH and haven't had problems going, stopping or avoiding sway. I try to drive the speed limit (and succeed) in most cases. I think I've got enough truck, but don't think I'd want to pull much more trailer than what I have. I've not noticed any issues with the factory tires. My guess is that if you run the numbers, you're going to be in the very tip top of what's acceptable, at best given your numbers above. Learn to run/understand the numbers above and you'll feel more comfortable about what you've got.
Also, the shorter campers are much easier to get around in tight spaces.
Always remember that free advice is what you pay for it. I can only relate my personal experience and wouldn't offer it up as a mantra for anyone else.