Unfortunately based on your suggestion, I was not able to get the music files working. As far as I can tell, the sound files appear to be loading in correctly, just not the music.
In the Music Pack Zip File, I have the following:
/assets/minecraft/sounds/music/game/(files)
/assets/minecraft/sounds/music/menu/(files)
/assets/minecraft/sounds/music/records/(files)
I tried moving things around according to your guide, but I think I might be missing something, it's not making sense to me