Welcome to the forum!
Few things. Is it really sway? And, if it is, it is better to cure the sway than to band aid it.
1st, is it continuous oscillation over a certain speed? Or, is it a push/pull feeling when trucks go by.
Have you taken it to the scales? I see this is a rear kitchen model, that is light on the tongue from the specs. A lot of people stock the kitchen with heavy stuff, taking more weight off the tongue. This is also a 35' long sail behind you.
You say you have a crew cab lariet. F150, F250, F350, F450.
Also, if you have an F150, do you have LT or P rated tires. Are you feeling the squishiness of the light duty P rated tires.
Could this be a combination off all factors??