If I'm not mistaken they make 430ish at the wheels and they weigh around 3100-3200 lbs. If you want to walk hard on one, you're going to need a lot more than just engine mods. You're going to need some serious traction. I think you can do it on the stock block, but it'll be pushing the limits.
My suggestion, if you're trying to do it as cheaply as possible, would be a h/c/i 302 with a 150-200 shot of nitrous, or you can keep the compression low and put on a stout blower or turbo system. n/a a motor like that would push 300 ish rwhp. With boost, going to 500ish at the wheels wouldn't be out of the realm of possibility. A TKO tranny, sticky tires, 3.73 gears, and hardened 28 spline or 31 spline axles. You should consider
suspension mods at this point too, but you can get away without them if you're just trying to beat a stock Z06. Then lighten the car to 3000 lbs or less. I think that combo would walk pretty good from a Z06 from a stop or roll. From a stop, you will annihilate him out of the hole.
You didn't ask this, but... From a roll you won't have anything on a new ZR1 unless you're pushing middle 500s at the wheels. From a stop, though, I don't think one could catch you in the 1/4. Your combo with traction should be knocking down mid 10s or better. Just keep the tune safe... 1 detonation event and everything is coming apart. Not to mention, you're already at the limits of the block itself.
Chris