Can you drive fast enough to make it go away? ...not that I would advise anyone to break the law, but this is one of the diagnostic tools we used to troubleshoot at the shop I worked at. Also, a ford dealer in the area here has a $60k!?!...? Hunter GSP 9700 (with road force measurement) balancing machine that reported other balancing data such as road force that even an apparently properly balanced tire could have that could cause a shake. The dealership is Superior Ford in Plymouth MN and they are better than most. Just a thought.
Karl
Karl