It is an interesting question that I don't have a particularly good answer for. Super Corvettes in the past here in America generally would be shipped pretty much stripped to the bone. Spartan interiors and exteriors, and the obvious addition of more power and a suspension that is dialed-in better than others on the road.
...What that would translate to, as you point out, is difficult to describe given the position of the Z06 to begin with. I think the obvious route for GM to take with this car would be to do something alike the 911 GT2, taking an allready powerful car and stripping it down to the basics. I'd expect a fairly stripped interior, the leather/suede seats now common to cars like this, fewer layers of sound-canceling equipment, possibly the lack of a stero (although that is questionable), and the "fix" for the quirky suspension found under the Z06.
...But with the Z06 allready being so fast to begin with, I just can't imagine how much faster this car would be with an extra 100+ BHP.
(crossing my fingers that she becomes the first stock Corvette to have a top-speed north of 200 MPH)