I had INVOs on a previous car. They don't last long, pick up a lot of stuff from the road, and are scary when its less than 60 degrees out.
That said, they're quiet for as aggressive of a tire as they are, have impressive grip in the rain, are reasonably priced, and grip pretty well. I don't know about 600rwhp well, but there's not much in a street-able tire that does well with that much power.
To the extent you can find and get a Pilot SS in the size you need you should do it. IT is simply the best tire out there. The problem one runs into was already mentioned by the fella above. If you are putting down 600 then NO street tire is going to give you dead hook capacity...none. Get DR's if you want a tire to street that has SOME tread pattern and rating OTW spinning will be early and often.
In stock GS/Z06 sizes the PSS are about $1400 a set. Mine have at least 7/32ds of tread with about 12k miles on them. Even if Nittos are $400 cheaper, over 30k miles or so the actual cost is practically nothing.
Turkey....have you considered the Michelin PS2 ZP...standard OE tires on ZR1s, 427s, and certain Z06s. They are pricey, but they are also runflat and perform just as good as the PSS IMO. Then you can get them in the correct sizes for your widebody.