Those are brochure weights you listed. Add 2-400lbs for post delivery. Now you're at 68-7000lbs dry. Add the typical 1000lbs of gear and you're at 8000lbs. Figure 12% for TW and your at 960lbs. Close to your trucks GVW. Did you figure in the bed cover in your estimates? IMO 8000lbs and 35' is too much for you F150. I towed 7300lbs and 31' with my 2010 F150 Super Crew 5.5 bed Max Tow and 1857lb payload. I was 50lbs under my RAWR of 4050lbs. 80% of the time it was fine. I did the LT tire upgrade and installed SuperSprings. Moved up to a 3/4 ton CC LB and it was a night and day difference. TT no longer wanted to moved the truck around.
My advice is if you're going to tow maxed out then invest in a Hensley Arrow or ProPride hitch. It will be the best money you spend on that setup. Better than LT tires, shocks and any suspension mods you will think you need to make because the TT is pushing your truck around in less than ideal conditions.
I might add also that with the rear kitchen most of your added weight will be in the rear. Which will keep the TW lower but may increase the chance of swaying.