I am not sure about the stabilizer thing, my Ex has one factory. I have not had the shimmy, I need the rotate the tires and check the air. I am starting to feel a slight vibration, but I think it needs a balance......
Could you be more descriptive of what the shake feels like, maybe mine is doing it, but some of the stuff I feel I chalk up to is "driving like a truck" Most trucks I have driven react the same way to certain road conditions.....