John, One of the CAC's Supporting Vendors is Spring Mountain Racing School. Click this LINK to view their website- the site mentions a program which allows to race your car on their track using racing skills they teach you. They're located a few minutes outside Las Vegas, NV, so they can offer year round classes and programs.
Why not give them a call and see what they have to say?
I have thought about that as well. However, I would rather wear the tires and brakes off a school car than my own. I suspect they have some kind of deal with tire and brake companies that will allow the driving schools to replace those things for cheaper than you could. I would like to take a driving school using cars just like mine, but not my actual car. Just my $0.02
This is a driving school where you use your car. I don't know much about it but I don't think it's a school where you learn to RACE. It's more of taking your car and putting it into skids and hard cornering so you'll know how it reacts. They go to Atlanta and to Charlotte. See web site below...
I took the 3 day "Beginners" class several years ago at Spring Mountain Motor Sports. What a blast. They had 2005 coupes, 2004 coupes and 2004 Z06s. They have newer Corvette now. I didn't use my Corvette. I have a convertible and have a long ways to drive it to Pahrump, Nevada.
I believe the Bonduraunt School in Phoenix will allow you to use your own car after it is checked out by their mechanics. When I took their driving school everyone used the schools cars. No sense in wearing out your own equipment.