Even technically the song wouldn't work. They wouldn't have room on stage to learn much.

They could re-work the song or create a new one, we need to know how she learns all of the information about her family.
Angela Lansbury should definately do it, it is HER role.
Kerry Butler could also be Anastasia, LOL.
"The Spectacle has, indeed, an emotional attraction of its own, but, of all the parts, it is the least artistic, and connected least with the art of poetry. For the power of Tragedy, we may be sure, is felt even apart from representation and actors. Besides, the production of spectacular effects depends more on the art of the stage machinist than on that of the poet."
--Aristotle