What luck!! I did just the opposite - hauled an S-Class from California to Ohio. We should have coordinated, and we could have stayed where we were
Anyway, I had a moving company haul the Benz inside their moving truck, since they were "dead-heading" anyway. Then just last month, I sent an auto to my brother from Ohio to New Jersey, and that cost about $550.
I'm afraid that if you are set on shipping a car, it might cost you about 90 cents to $1.00 per mile - the Teamsters seem to have flat rates for such hauls, and any quote seems to vary by only tens of dollars, not hundreds of dollars.
Another option is to try to get a college student or professional driver to drive it to Cailfornia. Many transporter companies have this service, and it is much cheaper than hauling on a truck. If you need any more information, please ask.......Andras