The Yorkie rescue in NC might want to contact PETS, LLC
P.E.T.S. LLC - Animal Rescue Road Trips
and see if they might be able to help when they are running empty back down to the south.
The other possibility is the volunteer transport groups that can be found at can be found at Yahoo groups. Again it would have to be the rescue organization who would have to make the arrangements and contact some transport coordinators.
If you want to send me a DM with the contact info for the Yorkie rescue I can assist them if they are not already familiar with the volunteer transports and don't have any contacts with coordinators who would put together the actual run.