The shimmy or violent shaking that you are describing is all to familiar to me.
The easy fix for this is actually to replace your engine mounts. I replaced everything on the front suspension on mine and still did it. I know that it has something to do with the front axles binding or being out of balance. New engine mounts changes the front half shafts angle, thus changing the condition.
I tried re-clocking the axles several times and had no luck fixing it completely.
The other thing I never had a chance to do before I got rid of the car was, I found a old merced Red fiche for a vibration that recommended replacing the suspension bushings and clocking them the wrong way to stiffing the suspension up.

Good luck, it scares the hell out of you when it does it.