Assuming that most of the flying will be over the audience, I would think that they would need a theatre with as much "head room" as possible, which really only leaves about 5 to choose from, Hilton, Palace, Broadway, New Amsterdam, Minskoff, 2 of those definately won't be available anytime soon.
Personally the Hilton would be the best since it has the most space, it's a double balcony and the balconies are rather small.
http://www.flickr.com/photos/27199361@N08/ Phantom at the Royal Empire Theatre