Coast-to-coast shipping for $1,200 sounds about right +/-, but for open trailers. Enclosed shipping might be a few ($200-$300) hundred more. BTW, these companies cater to the fancy car crowd too.
BTW, right now for the next 2-3 weeks, you may have a more difficult time finding shippers with space, which means higher prices. August 17-20 is the Monterey Historic Races and the Pebble Beach Concours in Monterey/Carmel, CA. Typically, a lot of expensive cars will be moving West before 8/17 and a lot of expensive cars will be moving East post 8/20. With the car shows, auctions and racing, Monterey in August in one of, if not the premier, auto event in the US each year.