Boulevard

By far your biggest improvement will be in the weight distributing hitch so concentrate on this right after you have checked your trailer tires. Garbage trailer tires make for a wobbly trailer so its good quality brand name trailer tires first then its off to see Blue Ox for some heavy duty high quality hitching. I use a Blue Ox with 1500 lb bars on a 6000 pound 26 foot trailer and an f150 which is very very similar to yours and locked is the best way to put it. Truck and trailer move as 1. Absolutely no sway, no wallowing and no gimmicks just bone stock f150. If you still cannot stabilize your rig than skip the RAS and the bags go straight to a good quality name brand LT rated tires. After that check out adding a long leaf. I know that that adding a leaf is out of fashion and that a lot of people love the RAS and the air bags and I am not knocking them but I like a good old fashion leaf spring. A good spring shop will bend you up a custom long leaf spring right in front of your eyes and help you set the truck to the height that you want while at the same time helping you with selecting the proper spring rate. Thicker springs with slight bend and thinner spring with large bend have different characteristics and they will explain this to you. Stick to the basics and keep it simple because those are the 2 things that will never fail you.