The Widow - The Mars Volta.
I think Matt's voice would make this song even more intense than it already is.
And as for Elton John covers, I think that "Original Sin" would be the very best choice. It's beautiful, but has plenty of scope for a traditional Muse "goin' maaaaaad" workover.
Also, I can't believe that nobody has suggested an Annie Lennox cover! I think that "No More I Love Yous" would be brilliant, or else "Love Song For A Vampire".