I would fly out to California even without having a specific car to look at and feel pretty confident that I would find something, if I could spend a day or two there. Fly in with a one-way ticket and rent a car at the airport -- with a list of autotrader ads and a rental car with a navigation system, you could probably check out a decent number of cars in a day (call the guys ahead of time and try to see if they will be around when you're in the area). If you want to see more cars, or some of the guys weren't available on the first day, stay the night at a cheap hotel, wake up, and check out the rest and decide on a car that day. Buy the car, have the guy follow you to the nearest rental-car location, and take him home. Then, gear up for a long-ass drive home in your brand-new Rex.
It seems like there are enough great looking CRXs in SoCal that you don't have to go out there for one you purchased sight-unseen. Maybe pick 3 or 4 cars that you want to check out. That way, you can be sure that you're getting the car you want (and be confident about it getting you back across the country). It sounds like a good time, really

If you're not 100% sure that you will find a car you like, buy a round-trip ticket instead. It's probably not that much more expensive, and you won't get treated like a terrorist for having a one-way). This plan won't be that cheap, but neither is shipping a car that you've never seen across the country and hoping for the best.