'Which is as Fate to all Things Else’

[Raynor]

This would mean that the actions of Men are predestined by Iluvatar, but were not a part of the Music played by the Ainur.

I disagree; this would imply that Men can act with impunity (cf Myths Transformed, Men are free from the consequences of their actions only when the intention is good and all possible effort has been performed).

Free will is guaranteed for Men, as stated in letter #181 and:

Originally Posted by Letter #153

Free Will is derivative, and is.'. only operative within provided circumstances; but in order that it may exist, it is necessary that the Author should guarantee it, whatever betides : sc. when it is 'against His Will', as we say, at any rate as it appears on a finite view. He does not stop or make 'unreal' sinful acts and their consequences.

It is true that Eru is named the only wholly free agent, but that is because he can make exceptions to "all rules and ordinances".