Glad that you understand tires are more important than size, a 245 R comp will outrace a crappy 305 all day
I am a big believer of grippy tires, I just don't like to pay for them....
I wouldn't bother with the R888. They might show tread on them, but they lose their useful life within the first five major heat cycle. I made that mistake three times, RA1 is a much better tire.
The 370 turns in quicker than the 350 for sure, but the 370 just plows and plows where the 350 felt more neutral (square setup). The 350 did have less rear grip (was on 235/45/17) and a much tail happy rear suspension, but it just felt much more fun to drive as you can get back on the gas much sooner. RE11 in 285 is plenty for a stock Z that is not on the track in the rear, you just have to get the proper front tires to match it.....
Here are some autox video, the back end does not break loose.....
YouTube - 370z autox
YouTube - Tom driving the 370z