Damn, I've been volunteered to setup an Autocross course that day.
I hear ya about being tight and the girth of a GC. I will say that the 'thrill ride' I got during the SRT Track Experience was much better in the GC than the Viper.
The Viper was everything you might expect, but when the instructor did a lap at Road America in the GC, HE NEVER TOUCHED THE BRAKES

He just lifted, twitched it sideways, and mashed the gas down again.