Congratulations on your new baby!!!!
I would recommend you call the hospital you are interested in and tell them that you would like to deliver there because you heard such wonderful things about them. Tell them also about the doctor situation and see what they say. I can't imagine they'd want to turn you away- it is a business, after all ;)
A possible alternative (although, admittedly, this might be a bit of a stretch) is if you know someone who has delivered at that hospital, ask them who their OB was, and did they like him/her. You could call and see if you can switch. I don't know if they'd want to take a new patient that is so close to delivering, but you won't know if you don't ask.
If you plan on having other children, you should find an OB that is affiliated w/ the hospital you want to go to. Same goes w/ all your other doctors. If you ever get sick, and need to be admitted, you don't want to be stuck @ a crummy hospital. I have to drive 30 min. to see all my doctors for just that reason, but it is so worth it to me.
Very best wishes to you and your family! :)