This debate of Men changing the Music and changing Eä could be resolved if we think that Eru foreknew the changes Men would make when he made the Third Theme.
Of course, this would make some people think that Men do what Eru just sung/played, and therefore, they are just robots of an omnipotent, omniscient being.
But predestination and prescience are not one and the same. One can foreknow without actually laying the path for the event.
Since we are all time-bound beings here (unless someone's not speaking up) we need an example. If I see a muon, I know that in 2.2 microseconds, it will decay into an electron, a neutrino, and an antineutrino. Now, this foreknowledge of mine does not mean I did the actual decay, because the muon is wholly other from me. But I can respond to it by photographing the decay, or something else.
Now, how does this apply to the Music? Perhaps Eru, unbound by time, saw the future at the same time Ainulindalë raged on before him, and introduced a new theme, one based on the actions Men would take when confronted with a certain situation.
But does this mean Eru made Men do certain things? No! As I said, the muon is a thing wholly other from me. And to Eru, Men are other.
Then Aulë took up a great hammer to smite the Dwarves . . . But . . . the voice of Ilúvatar said: 'Thy offer I accepted even as it was made. Dost thou not see that these things have now a life of their own, and speak with their own voices? Else they would not have flinched from thy blow, nor from any command of thy will.'
TS 2 - emphasis mine
Post-traumatic possum.
H-I, I shall be reacting to your "Two Wills" post soon.