Are you staying at the BC or YC? I would just ask to concierge to see what they can do for you.
In May 09 it was pouring and we didn't want to walk into Epcot for our Rose & Crown ADR for dinner. When we got back from the park that afternoon we asked the concierge desk (at the YC) to see if they could get us in Cape May for dinner instead. They did so, no problem. They also cancelled our Rose & Crown ADR for us.
They also got us Yachtsman Steakhouse that same trip and cancelled Calif Grill for us (again, it was due to it raining cats and dogs...as my daughter kept saying). I believe when you stay at a resort, they go out of their way to help you with their own restaurants.