The reason I like Cohen's the best is because of the backing singers. I think this song works best when there's the graceful and harmonious support of the backup singers... it adds to and "load balances" the hugely majestic tones of this song! I think when KD Lang or anyone does it solo, they're taking on too much, and while they might do a fine job, it's a lot for one person to sing. Just my thoughts!

I'm not enough of a fan to know how many of those verses he did sing in concert, but I do know that I have two recordings of him singing the song and they only have one verse in common. Weirdly, this verse ISN'T in the Jeff Buckley version. And it's easily my favorite:

    And even though
    It all went wrong
    I'll stand before the Lord of Song
    With nothing on my tongue but Hallelujah

Perhaps John Cale might still have them because Cohen faxed him 15 pages of lyrics - https://en.wikipedia.org/wiki/Hallelujah_(Leonard_Cohen_song...

NB. It's the version by Cale which became the basis of the later covers by Buckley, Wainwright, etc - https://www.youtube.com/watch?v=Nzu4LE667VM