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With new rubber and wider track ... you probably have a lot of slop in your various steering linkages. I know I have bad shocks, and find my steering is really loose at 60-65 MPH ... below and after that speed everything really tightens up.
Surely you had the alignment adjusted. That's adjusted, not just checked. All three angles, especially castor. By someone who knows what they are doing. I believe in keeping my castor up around 1 1/2 degrees positive. Less castor or even negative castor make the car more "responsive" but will make it wander or dart from side to side.
Also, if the 255/60s are different from stock in width or height, then the intersection point of the steering axis with the tire centerline is different from design. This will affect the toe-in/toe-out push on the tire. You will need to set the toe adjustment different from the factory specs. For example, a wider tire will move the intersection point further into the ground. This will create more toe-out push on the wheel. To compensate, the adjustment should have more toe-in than specs. And it's a trial & error thing to get it right.
How fresh are your suspension bushings?
I replaced all the front end suspension parts, but my car still would dart left and right unexpectedly. I had the car on a friend's lift and he pointed out that the rubber bushing had squished out and that the cross shaft was floping back and forth in the metal bushing shell.
So do all the usual front end checks, but keep this one in mind if all the first line checks come up fine
"TEACH"
Go to: http://www.corvettefaq.com and look under Suspension and Steering. Go to Steering Gear Adjustment - In Vehicle. Also Strg Gear Adjust Pic 1 and 2.
There is also a more exact adjustment that is done with a torque wrench and it is completely described in the Chevrolet shop manual.