Because you have the Z06 wheels, what do Z06's normally run out back? A 275 on your front is what I run in my rear! Wait...that sounds bad...my car has 275's out back from the factory (as would yours as I'm sure you already know). Is the stagger, or offset, of the Z wheel biased so you can run a wider tire without rubbing the fenders or inside the wheel well?
Ok, did a little Wiki job. The factory size tires for a Z06 are P265/40ZR-17 for the front and P295/35ZR-18 for the rear. Rims widths over a base C5 are increased one inch to 9.5 front, 10.5 rear as stated...nothing on offset though....
I don't see how going to a 305 would cause anything to rub as the tire section width is increased only half a cm wider on both sides. A problem could show up if you went to a taller tire.