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Not sure why they would want the higher aspect ratios? The lower ones will flex less and improve the handling. Street tires will work fine for a good while. It will be the most fun you have ever had in your car. Make sure to upgrade your brake fluid and if you have ceramic pads, repl them with some metallic ones at least. You might want to look into one of these if you persue this much:
The thing that is going to cause you a problem is roll over protection with a Vert. Every organization that I run with requires a proper roll bar assembly on convertable cars. Check out the regulations at the track and specific group that you want to run with.
I agree w/CHJ - most groups running HPDE events will require a roll bar to run a vert. Check exactly what is acceptable in terms of material & installation specs before you buy.