Wow - it took a while to get a bid that I was able to accept. Plenty of people willing to do it for the regular prices that I can book every day, but waiting for someone who does it for a few hundred less - that took a while.
In the end it all worked out, and it was a good experience.
Moral of the story - don't be in a hurry, or you'll pay the same price as calling a regular shipper.