I have NT05's on my Z06 they are non runflat and work well. Michelin PS2's are another option.
Since I have never run the G2 F1 supercars I don't know how they compare strait line and lateral grip. Both those options I listed are better than the G1 tire that cam on my Z06 IMO.
these all have issue at cold temp with grip though. I never had any storage issues with PS2's or NT05's though.
2013 ZL1 -sold
2013 Megacab 8" lift 38"mt's