I would blame the front tires for that instability.  My F-1 Eagles Supercar tires tend to follow the "ruts" worn into the pavement, more so when they are begining to wear out.  I am into my second set of tires on my '07 C-6, and when brand new, the instability dissapears.  As the tires wear out, it begins to be very noticeable.  I might go with the new Pirelli's or Michelin;s.

I found the standard suspension of my '07 C6 to be a bit soft and twitchy, especially when hitting some bumps or uneven surface while negotiating a curve. This is what you may be noticing, and is one of the reasons that caused me to trade in the '07 for the '08 with the Z51 performance suspension. This resulted in an extreme improvement in handling.

SO are exactly the traits I have been noticing with my F1 tires. Thanks both of you let me know if another tire does better.

those are the traits LOL

I would check the front end allignment. My 05 with Z-51 handling package started doing this at about 4,000 miles and was real bad by 7,000 miles. Got my dealer to do a complete allignment and this took care of the problem. C6SilverBullet