For the time being then, I'd stick with rhymes instead of songs. He may be sensitive to some pitches of music, but spoken rhythmic rhymes, like Jack Be Nimble or Pat-a-Cake or other nursery rhymes, can still give him a sense of rhythm while the hearing matures. You can also "say" some songs like rhymes, like Itsy Bitsy Spider, with the motions.
Any chance of fluid in his ears, as PP suggested? It would distort sound and make it possibly overpowering, like hearing a song in an echo chamber.