Look at the rating on your hitch. It will not be rated nearly as high as you think with weight carrying. Can you haul it without the weight bars?? Probably. Should you since you have the correct equipment?? No, use the right tools for the job!
My TV is a 1 ton Dodge with airbags and I have hauled over 10K on the hitch by itself. It did just fine but I would never haul my camper that way for any distance.
BTW, explain that electronic sway control? I don't understand how anything on a truck can help the sway of a trailer.
Chris