Numbers are the first step and very important step but that doesn't guarantee you will have a safe setup. I went from a Prime Time 5er 35 foot long weight in round 13,000 pounds loaded ready to camp. Pulled great even in 30 mile per hour side winds and didn't move even an inch when a Simi past. Traded it for Montana 3711FL that measured 42 foot long weigh in at around 14,500 ready to camp. Was pulling it with a 2015 Ford 1 Ton diesel. My Ford 1 Ton diesel was Super Cab with 157-inch wheelbase with 3744 payload rating and the Montana was 150 pounds under my GVWR and 800 pounds under my rear GAWR. So within all numbers and it gave me lots of white-knuckle moments in even 10 to 15 mile per hour side winds and a pass Simi would move the wag the dog. Tried sway bars, rearranging the contents of the 5er, increase air in tires and nothing work. I come to the conclusion that it was the length of the RV and the front living room floorplan with less forward of the axle weight and the short 157-inch wheelbase. Put in a friends DRW and even 35 miles per hour side winds didn't move it. Talk to a couple of people with just the SRW long bed and they didn't have any problems towing.. We traded Montana for Solitude 34 foot and got caught in I10 in 40 gusting 55 and didn't have to pull over.
I guess all the babble that being within specs is good by it doesn't tell the entire story. The length and Floor Plan can make a difference even when all the numbers are within range.
Edit My 2015 Ford 1-ton Diesel had hitch rating of 1250 pounds lower than your F150. My GMC 1-ton diesel had 1800 pounds rating.