There is absolutely no space that I am aware of in NYC that could accommodate this production, at least as it is currenlty staged in London. A theatre like Circle in the Square, in addition to not being large enough for the physical production, does not hold enough seats to be commercially viable for a show with this large a cast, crew, and orchestra.
Also, the staging is fun, but what really makes the production soar is the cast, especially the actors playing Sky and Sarah, who I'm guessing wouldn't be brought to NYC with a transfer.
It should be left where it is, and yes, it would be brilliant if NYC eventually built a flex theatre space like the the Bridge.