Phil, one other theory that might make sense. You said you have more sway, which I take to mean, it had some sway before the tire swap? If so, the lower rolling resistance of the r250 may make whatever is causing your sway to be more pronounced? Kind of like when you apply just the trailer brakes to straighten out a tag trailer when it is swaying a bit. I have a triple axle toy hauler, with 6 tires on the ground it felt like the emergency brake was released when I swapped from ST's to the R250's.
Kind of odd, most posts I've read state 5ers are a very stable tow. Have you checked pin weight to see if it is in the proper range for the weight of the rig?
Best of luck getting to the cause of it and please post up when you get it figured out.We all learn that way. Safe travels, Mark