I carry a regular draw bar in my truck, but it only has a 2" ball on it for my little utility trailer..
Never thought I'd have to use it for my TT, but if I had to, and I could swap the balls, it would work for my TT..
But I've had my EAZ-LIFT WD hitch for over 15 years now, towing my #5000 TT, so never an issue there.
No 'sway bars' either..
But, if the 'sway bars' work for you, use them.. That's all I can say.
Good luck!
Mitch
2013 F150 XLT 4x4 SuperCab Max Tow Egoboost 3.73 gears #7700 GVWR #1920 payload. 2019 Rockwood Mini Lite 2511S.