I called the Art of Animation number (407 938 7000) and the girl there put me through to the general réservations number (407 939 1936) so if you want to call to request a building or room or anything not on the check-in form, I guess that is the one to call. She said they don't do réservations stuff, it is all central.
The CM checked and said that there was no availability for those dates, but he put the request on my reservation form and said if one becomes available they will try to meet our request.
Now, I also checked the website for my dates and there are Cars rooms available. So I am hopeful that the 'no availability' means that we don't get to pick for my type of package (
Free Dining) not that all of the actual rooms are full. I think they will assign us a room based on what is available when the date arrives. For the record, he didn't say what kind of room was available either.