Argh. I couldn't wait any longer so I found a walkthrough:

Grapple across, walk up to the statue and hit R. Pick it up and put it down to get it to stop following you. Walk to the switch and stand on it to make a path appear. While doing that, play the Command Melody. You are now the statue.

I call "LAAAAAAME" right now. No hint was given that I had to do the command melody to this statue. Only prior hint was that I used it to open a door. What does remote-controlling a statue have to do with opening a door?

LAAAAAAAME.

/me deletes the walkthrough until I get stuck again...