[villagetinker]

Use Google maps, and put in your new address, then in the search field enter trucking company, and see what comes up nearby, and start calling. I went through something like this back up north, and the big sticking point was insurance. Every company that had a dock, was not interested because of possible liability insurance.
On a side note, I have never heard of a moving company with this restriction. I would go back to THEM and say if you want the contract, YOU find place to unload, however, this does not cover how your stuff then gets to your house.
Good luck, I think you are going to need it.