Try www.intercitylines.com they can give you a quote. I think they have both enclosed and open carriers. There are many other companies that do this also. Try a search on "auto transports". I believe I saw one example of $800 from Chicago to LA
The reason i cant get my scca car sold is because no one wants to pay the shipping to back east. Im in cali and the quotes i got where around 1900-2600. The car is light also because it doesnt have engine trans or diff. other than that its in tact and thats how much they wanted.. Just for a stock L28 they want $248.
I know I'm a little late here, but I had my 66 lincoln shipped from arizona to virginia and it cost me 1000 bucks... not bad for a 6000 pound car. I went through AAA also. I'm sure you can find something pretty reasonable if you look hard enough.