Many of the United Van Line type movers take cars, especially if they're not full or it's "off-season" in moving. call your local united van lines or 1 in fla and see if they can help. I used Liberty Moving on Long Island when I moved across country 2x and both times they offered to ship my car with my stuff.

you can also try here:

http://www.movecars.com/toc/find/index.htm

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