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I can only speak to the base (non GS / Z06). As I was shopping for a second set of wheels it became clear that the offsets and calipers make it impossible to have any concave shape without having the wheels stick out from the body.
Unfortunately no. The engineers pushed the wheels of the C7 out as far as possible on each corner for improved performance so the offset won't allow the deep dish or highly concave wheels designs from previous generations.
Forgeline has some nice wheels that have a partial lip, but nothing with a lip like the C6 or C5 aftermarket wheel options like the CCW 505As I have on my C5 vert.
Yeah you can't have much lip past the spokes. Best bet is to find an open design wheel that is cast with a deep lip behind the spokes. In a light color you see that deep lip. These are Cray Brickyards with 265&305 Pilot Super Sports. It took some work to get the right stance. Ride height is dropped 1", spacers removed behind rear upper control arms, camber set to max street spec of -1.8 degree, inner fender lip shaved, fender bracket behind rear wheel moved out. 6mm spacers in front.