Listen to Dmitry
 

He said it was the wheel bearings/ hubs that caused the high speed shimmy and I didn't listen.
My mistake was to check the car with the wheels cool - no noticeable play when shaking
the wheel from the top - shaking from the sides tests tie rods.
After a 100 mile run - staying under 80 mph the shake speed - I could easily feel the play in the bearings -
So the hubs are on order and I have a cool steering rack from an e36 and the Pellican kit to install but this is a really tough job. Will probably get tie rods and all the front end stuff in the future for a winter project.

We have two ears and one mouth so listening is important.

Tom