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The sways, springs and shocks on any C5 and or C6 are designed as a package. If you go to a bar that big, you really should have a tire/rim that is much wider than stock. As you can see the ZO6 package has bars that are a good deal larger than the C5 base and they incorporated a larger size set of wheels and tires. They also have higher rate springs and improved shocks.
Unless you get some higher rate springs and some better than base C5 Shocks, you may be hurting the cars handling performance.
The track that the cars drive or race on with really high rate spring and sway bar rates are pretty smooth and don't have any nasty irregularities. With those bars and the springs and shocks that should be combined with, you will be will give yo a really rough ride and may cause you to loose tire contact in some situations.
Many say C6 Z51 bars are the sweet spot for a balance between aggressive and comfort. If I were going after a very street oriented car, I'd do C6 Z51 bars, C5 Z51 springs with DRM Bilsteins or C6 Z06 shocks.