I much prefer an earlier version of this (Cohen rewrites obsessively) that Cohen himself sang. Verse 1 and 2 are as you have them, but then:

3) You say I take the name in vain --
   I don't even know the name,
   But even if I did, well, what's it to ya?
   There's a blaze of light in every word,
   It doesn't matter what you heard,
   The holy, or the broken, Hallelujah.

4) I did my best -- it wasn't much:
   I could not feel, so I tried to touch.
   I've told the truth. I did not come to fool ya.
   And even though it all went wrong
   I'll stand before the Lord of Song
   With nothing on my tongue but Hallelujah.

Hallelujah. Hallelelujah.
Hallelujah, Hallelu-u-jah.

It ends there. I find it much simpler, clearer and more exciting than later versions.