From the novel I find that the actual climax of the story happens after the moment of highest dramatic tension, which is way weird but novels are allowed to do that. Since the story is all about Frodo getting home, just doing something to get his life back to normal, the climax seems to come when he gets back to the gates of the shire to see everything has changed, horribly changed.
Now as a musical they will have to change the story line to be all about the destruction of the ring. Where the climaz would be able to happen at the highest emotional point...ehh whatever....sorry just felt like rambling for a while.
STEVOS
"IF I TRY THERE MAY BE A CHANCE / WE COULD LOVE WITH OUR EYES CLOSED/ WITH OUR EYES CLOSED WE COULD CHANGE THE WORLD!"- Stephen Dwight