Nearly the same issue here. Excessive vibration....worst right around 70 mph. I thought it might be an alignment issue, so I took it in to the dealership. They did a wheel balance, which didn't really help. Switching over to my winter setup confirmed for me that it wasn't the wheels, since it's still there. I can't say that it's coming from a specific side, so there's really nothing cuing me in to anything specific. Main difference is that mine doesn't go away if I restart the car.
Any ideas?