Well I think I've got it. It's not a particularly difficult initial solve, and the down phrase emerges early enough to help with identifying the extra letters.
But it's the endgame.
My version works in that I can exchange the four pairs of letters, four from a column and four spread out in a row.
Then I THINK I move the now-vertical four to a symmetrical place on the grid, which I THINK shows it can't do what the song says.
That leaves the bottom line, which I can fill with the alliterative phrase from the song, so long as I obliterate word one.
While I can't see in the rubric that that's (obliterating) what I should do, anything else doesn't work. The unchecked letter match and I still end up with words everywhere, so that "apart from the final phrase" worries me a bit.
Referee?