Affordable Shipping Company?

[Mycallways]

I am in process of trading in my car and purchasing a new (preowned) one all from out of state.
I will have a shipping company bring the new car to me, and then have mine shipped back to the seller. The distance is about 1200 miles one way. I've spoken with the dealer who recommended a couple of shipping companies, but they charge $750 each way minimum. I've looked on Uship and found rates of $400 each way.
Does anyone here rec a reputable shipping co. that has full insurance and reasonable turn around time that won't cost me so much?
Thanks in advance.