Ever used that fix-a-flat stuff? If you have it could have settled into one section of the tire. In my old car I didn't know any better and used that stuff. It did what you've explained... slight movement in the steering wheel but still going straight, be pretty shaky around 40mph or so and then smooth out around 70mph (less variance) and then get worse quickly once I hit a few mph faster. In corners the inertia isn't being xferred as much into the suspension with the higher profile tires I had (I took corners, ummm, fast), it's going into the tires a little more.
Just a thought...