There used to be an outfit called something like Driveaway that would match people wanting/willing to drive across the country with people with cars needing to be moved. It once was a standard thing for students to do. I don't know if they're still in existence.

For an expensive car, I'd start with suggestions from your car dealer. However, shipping a car in a closed vehicle isn't cheap, although car dealers seem to be able to arrange for the dates they want without too much difficulty.

If your household is also moving, major long distance movers can just load the car into the truck with your other belongings.