I must admit while walking a ZO6 Corvette last night with relative ease my higher speed jaunts were quite smooth. Much better than the last 420 we were testing. Nothing worse than a shimmy at high speeds.
I have found that when getting into tangles with other higher output vehicles it is always best to get the jump on them. Thats why I dont mess around. Still I yearn for a wee bit more.
Best of luck finding that shimmy. I would try the new tires and balance however if that does not take care of it you could be due for a set of bushings. Flex disc's must be inspected for cracks. It is WAY PAST time to change them if you can see string looking frey.
Also important are the brake support bushings, and rear sub frame bushings. I have seen these cause a shimmy.
And last but certanly not least, "A good alignment when all is said and done" and you will be back in business.