I think I had a similar shimmy in the front. Mine was steering rack bushings...yours might be the same. But at high speeds, even slight imbalances make a big difference. So yes, unbalanced tires could make a difference.

 

Was uit the streering wheel? or the car. And how much did you pay to get those replaced

 

Has anyone here with a 2001 reused there strut mounts? I know that the 97-00 es300 had a different strut mount then the 01 an are the only ones ive heard who have replaced the mounts with the struts