Need help picking tires: ZR1 Wheel: 20x12, 19x10

Hey guys!

I'm a little torn as to which tire to select for my 2006 Z06 that has ZR1 wheels on it. They are 20x12 and 19x10. I have a built motor putting down ~800rwhp so traction will be a serious issue.

I can't decide between the non-run-flat Nitto INVO and the run-flat Michelin Pilot Sport Cup 2 ZP or SS...

Am I ok to go with 345 in the back and 285 in the front? I don't want any rubbing issues. Any recommendations on what I should get or where I should go? I like driving on back roads so a non-radial is out of the question unless I switch wheels/tires at the drag strip.

Thanks!

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Need help picking tires: ZR1 Wheel: 20x12, 19x10