Elijah seems unconcerned about getting his violin back. Why?
Unlike all of the other characters (except, ostensibly, Old Woman), Elijah has no family. So I think the violin fulfills the role of his "child". He does not want to keep it forever - that would be an unhealthy relationship. Rather, he tells the protagonist King: "You will repay me in full, for your daughter will set free the imprisoned melodies." Elijah's wish for the instrument is not to continue to possess it, but that it should go forth into the world.