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Increasing the size of the rear tires adds rear grip which increases understeer. In order to restore balance, i.e., reduce understeer, you would want to install a larger rear bar. If you are mostly drag racing I would just leave the bars as-is as the only place you would notice the difference is on the road course or at an autocross.
The base rear bar is to light for the C6 and causes the car to wallow as it exits a corner. Normally I suggest the Z51 bar on a base as the Z06 bar has a tendency to induce oversteer near the limits, but in this case with more rear tire the Z06 rear bar might work better.
Whichever rear bar you choose the front sway bar also needs to be upgraded to match. The Z51 and Z06 share the same front bar so that's a no brainer.
Is it under or over steering now? I’d assume understeer with the giant tires. Anyway you aren’t clear, do you want more understeer or less. Bigger bar in the rear will increase front grip, and vice versa