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Shipping is best, but if you have to go with the flatbed, I agree that every bit of crap on the road will be thrown up at the front of your car.
Put a bra on your car, if you can rig up a metal or plywood shield on the front of the trailer, do so. Do NOT put a car cover on the car. Wind will get under it and rub it against the paint and by the time you get to the west coast, you'll need a new paint job. Covers aren't made for moving like a bra is.
You might think about using that blue painters tape on as much of the front as you can. Some here have tried that and found it works pretty well. I have no personal experience using it that way.
Designer Imagines A Corvette That Looks More Like a Corvette Than the Corvette
Slideshow: A Jaguar designer's personal project imagines what a modern front-engined Corvette might look like if Chevrolet revisited the golden age of the Stingray.