You need to get some actual weights on your rig to tell a few things, but just guessing off the cuff, it sounds like you might not have enough tongue weight.
The "anti sway control" built into the F150 is not meant to dampen any slight wiggles... It's meant to help you control a situation where you are in a really serious sway condition where you are on the verge of crashing.
The "sway bar" you have on the rear axle of the truck is meant for cornering and is actually a "anti roll bar" to help keep the body roll to a minimum.
Finally, the EQ hitch you have might not be setup properly?? Do you have a pic of the hitched up rig?
So, lots of things it can be, or maybe you are just ultra sensitive?? To me, "sway" is when you are see sawing the steering wheel to gain control over the rig... If all that's happening is you feel a wiggle or a tug or pull from the trailer when conditions warrant, that's just what's happening at that time and may or may not be 'normal', but is not a condition that should cause an out of control situation either..
So, get some actual weights. Get a pic of the setup and maybe slow down a bit?? ;)
Going 60 mph compared to 65 mph is not going to cost you that much time/distance in the long run...
Good luck!
Mitch