I moved from SF to Melbourne last year and had a very good experience with Stevens International. They were the cheapest company we got a quote from, and everything went very smoothly. We had no surprise costs, the shipment arrived on time and everything arrived intact, including boxes of china. We got their name, as well as the others we got quotes from, from movingscam.com, where they had great reviews.
I hope that helps. Good luck with your move!