The Ford "built in sway control" is for the worst case sway situation, like you are see-sawing the steering wheel and out of control.. I have it on my F150, but it has never kicked in thankfully!
It's not a substitute for a mechanical sway control built into the WD hitch setup.
That being said, when you say you have a #4800 TT, is that loaded up going down the road or what the "dry weight" says?
Don't really know what you mean by "heavy duty tow package"? Ford has a regular tow package, a max tow package and a heavy duty payload package.
Other factors in controlling sway is hitch setup, loading and proper tongue weight.
Good luck!
Mitch
2013 F150 XLT 4x4 SuperCab Max Tow Egoboost 3.73 gears #7700 GVWR #1920 payload. 2019 Rockwood Mini Lite 2511S.