Sure you can buy stouter tires and jam sections of well casing between the frame and axle to keep the truck from squatting, but you may never get things to where you will be happy with the results.
It's a very expensive guess. The whole point of looking at things on paper is so you can get an idea of what you're in for BEFORE you spend the money. I'm glad these guys who are just telling you to go for it and prop up the truck have infinite money and can just keep throwing cash at the problem, but most people don't. Not everyone is made of money. Some of us have one shot to get this right.
Right now, 1660 payload vs. 1375 EMPTY pin weight, it's not looking good. I don't consider GVWR a stone wall not to be breached, but F150s don't have the "hidden" payload capacity of an F250 or F350. It's more like 400lbs vs. 1000lbs+ on an F250 and a ton or more on an F350. You're going to be into your "hidden" capacity just towing the empty trailer home from the dealer with the family in the cab of the truck.