I've shipped my car a few times using
this company. For a 700-800 mile move it cost me $600. They've always given me good drivers and taken care of my car. You'll need to be a bit flexible with scheduling though, they might find someone to pick it up tomorrow, or a few days from now, worst case it might take a week or two to find someone. So if you're planning this out at the last minute that may not work.