You generally can't find much better for steering tires than Michelins.
Have been using the brand for over 20 years and that is what my new Ford come with. Will have to check the model tomorrow.
From your description I have feeling your problem is weight distribution.
I had my dually with 6500lb camper at 80 mph and handling perfect without real modification (couple of hockey pucks just in case). The only thing that keeps me from using downgrades at higher speed is fear that the camper might fly out.
In your case I would start with drive via scales.
