Robb, all 4 of yours do that? Mine are all nice and smooth while rotating. The only problem I had was that the rallyes I have are powder coated and at our car shows the judges might look at the valve stem being centered. So,,,,, I would mount my tires, have them balanced, then drive home, look at the tires, and the rears SPUN around a little maybe up to a 1/4 turn. This would also throw off my balance. So I break the bead, turn the tire, and look at them 2 weeks later and they had spun again. After 3 times of this, I just laid a bead of black silicone sealant around the bead, inside and outside, and haven't had a problem since.
I also put a little paint dot on the tire, next to the valve stem so I can see if it moved.
Mounting and remounting was easy since I have one of those $35.00 bead breakers from Harbor Freight