All I can say about cheap shipping quotes, is ask whether your car will be stacked with others, where it will be stacked, whether crap will be placed in, or on your car etc. Thats why shipping prices can be cheap. Damages are likely when dealt with like that. Depending how nice your car is, you may be better served shipping it in a 20ft box by itself. Its more pricey, but the car arrives EXACTLY as you bought it.
No offence intended against John Cain as I do not know how he ships his items, but ask the Q anyway, for your own peace of mind.