It is not that hard to find someone who will bring your care for a good price. Usually there are many brokers that are searching for reasonable prices on the market but you can call an agency as well. So you can search for a
cheap shipping agency in United States and check for more information. Also, the price will be fixed in dependence of the characteristics of the car. So if it is big and heavy, don't wait for a lower price. I am sure you will find a good offer, because US is full of shipping companies.