Thanks, everyone, for your advice. Now I understand the allure of the UD! It sounds unlikely for us and that it might not be a good fit anyway-I don't want to disturb the "quiet zone" and while we are planning on sleeping you can never be 100% sure with kids.
Looks like I will be stalking the computer at check in.
One more question: I'm gold on AA, does that translate to any seating benes on BA?