So let's start with some conjecture hear. Not about the 60mph, that is explicit in the literature. About the gearing and power curve.
For the power curve, I will rely on Car and Driver and the published specs. Those spec show 443hp at the torque peak, 500hp @6200, and C&D showed around 450hp at the 7000rpm redline.
For gear...a little conjecture.
Transmission technologies lists only one T-56 with a high enough torque rating for the Z06. It has the same ratios as the Viper and the standard C6. So the assumption is that is the transmission. Of course, the C6Z may have custom gearing.
For the rear end, to hit 60 with a 2.66 first gear you would need a 3.15 rear. And it just so happens that this combo, with a 1.30 gear, would hit 127 in third. What a coincidence!
Now, the pros and the cons. The C6Z has a very flat power curve. for the top 30% of the rev range the power varies only about 12%. And it is the same at the redline as after the shift. Put in another way, you have the same acceleration in 2nd at the redline as you do in 3rd after the shift.
So, as long as you are in that range, it really doesn't help much to have additional gears. Once you hit the mid-4k range, assuming your tires are hooked up, nothing is really lost in the gearing. The question is, will you spin the tires until 40mph?
For road courses, that gearbox has a tighter spread from 2-3, 3-4, and 4-5 (23-27%). Those would be the gears you'd use and that box will give you a fair amount of flexibility.
Cons, cons...oh, yes, the cons. Well, I can think of four. First is that traction thing. If you hook up sooner, first gear is a little tall.
Second, the gap on the 1-2 shift of that box--2.66 to 1.78, over a 33% drop--is a little steep. Dropping the power a little further.
Third, fifth gear is along for the ride. With a huge 32+% drop between gears.
Fourth, if you modify the car, and more than a few should get header and cam upgrades, the power curve will continue climbing higher. The drop between gears will be significant, and that tall first and big 1-2 drop will be more of an issue.
Some of this may be mitigated by a little gearing legerdemain. A shift to a 3.73 or 3.90 rear gear should make this a complete 4-gear 1/4 mile car for a lightly modified (132 and 139 trap speed respectively) C6Z. Wow, it is hard to believe those may be numbers for a lightly modified car!
David