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Rick,
Talk to the Corlew dealership and see if they will let you use one of the racks there. They sponsor the Corvettes of Clarksville Corvette club and may be willing to work with you on this. You can do some PR for the club while you are there.
Good looking vette by the way
Neil in Tenn
I'd follow 71airstrikes advice. Having the car up and on jackstands at all four points is the safest way to observe a car running with the transmission in nutral.