The ZR-1 does not share the same trans ratios as Z06es. It's got a taller first gear and all the other gears, except fourth, are different.
I think the TR6060 used in the Z06 has its ratios pretty optimized for it's torque curve and the required reliability, but I suppose, if you were a hardcore drag racer, you could swap in the special 6060 used in Grand Sport manuals, which has a 2.99 first and lower 2nd and 3rd gears.
Of course, then the problem would be getting the car to hook and that, if 0-60 was important, you'd give up time because you'd have to shift. The stock Z06 trans and axle ratios are selected such that the car can go 0-60 in first.
I'm sure there are other choices in ratios in 6060s that a service shop experienced in working on TREMEC six-speeds could install.
The 3.42 axle ratios that all C5/6/7 manuals have with the 2.66 first gear makes for a final drive of 9.097 which is pretty good for a street car. I have no trouble spinning the tires with my C5 and C6, so all a lower ratio would do is spin them more unless I go to better tires.
Again, if it's hardcore drag racing you want, then yeah, a shorter gear, like a 3.9 or 4.1 might be a better choice as long as you had enough tire under the car to use the torque.