A really interesting essay.
I love that Tolkien made music so essential to Arda. There at the start. The very essence from where everything came.
And the discord of Melkor deciding to go his own way and make greater his part.
I believe that Tolkien himself said he disliked allegory, and yet the music and Melkor's discord run through everything as evil against good.
And I agree with you that all the songs and verses relate to that underpinning theme.