Shimmy in steering wheel

About a month ago, I started to experience a steering wheel shake while braking (12,000 miles) between 40 and 30 miles per hour. Otherwise, the truck was SOLID and smooth. Since I tow a boat from time to time I immediately assumed that my rotors were warped. I scheduled an appointment with Ford and dropped the truck off the next Monday. Ford machined the rotors and road force balanced the tires, called me and told me it is done. Well, the brake shimmy was gone when I picked it up, but suddenly I have a violent high speed steering shimmy while cruising between 65 MPH and 70 MPH that gradually comes and goes every 10 seconds or so and lasts for about 10 seconds.

So, the next day, I call them and let them know what's going on, they said they couldn't get to me until the next day. So at lunch I went to Discount Tire, assuming the balancing was off, and had them balance the tires with their "fancy" GSP balancer. After I picked it up, the shake was a little better but still there. I drove it for a week this way and after taking a road trip, decided I would go back to Discount Tire and have them balance them again and rotate them this time. They did this and it still shook, but this time it was MUCH worse than before.

So, the next day I called Ford and drop it off. They called me back and tell me it is normal. I insist on seeing the shop foreman and taking him for a ride.

After the ride, he agrees with me that the shaking is not normal and it is bad enough for him to tell me to drop it off the next day. Next day, I drop it off, they rebalance everything. Still shimmies. Foreman calls and says, "I have now seen it at it's worst and it is completely unacceptable." Now he schedules the engineer to come in and look. Engineer says it must be the tires and rims. They replace them with tires and rims off a stock unit that exhibit "4 lb force" and "11 lb force." But the "shimmy is still there, " according to the foreman. They then replace the steering rack.

After this, The foreman calls me and tells me that it is "considerably better, " but he would like for me to drive it and let him know what I think because he wants some miles put on it before he completes the job.

I take it and immediately notice the shimmy is much better, but still there around 65 - 70 MPH. It is weird because it comes and goes about every 15 seconds. Gradually starting and gradually fading away. It gets REALLY intense and happens predictably if I brake from 70 to 60 MPH. The foreman insists it is impossible for brakes to cause a shake that comes and goes. So he will not replace the rotors. I want to insist that we at least try putting different rotors on there. But don't want to be a jerk about it.

Anyone have any thoughts? A $50k truck should drive should drive better than this in my opinion. And it did until the rotors got machined. At this point, I don't want to drive it with my 1 year old in the car with me. I feel like something is about to go majorly wrong.