[Mithadan]

I suppose another way of saying this is that somehow Morgoth's curse is manifested through Turin's choices.

This is a truism. Turin (and his family) is the one cursed. The curse affects or colors, to some extent, all his choices. As a mediocre rock band from the 1970s said, if you choose not to decide you still have made a choice. One cannot distinguish between Turin's actions and inactions as all are colored by the curse. One can distinguish between the actions of Turin and those of other characters. Turin is cursed, the others are not, yet to the extent they interact with Turin, they get caught up in Morgoth's malice. Beleg does not die because he is cursed. He dies because he is interacting with Turin. This applies to the victims of apparent misfortune throughout the tale, whether it be Brodda, Dorlas, Gwindor, Brandir, etc.

Free will vs. fate. My favorite line on this subject from Tolkien's works is found in the Silmarillion, and it is an early conception found in earlier iterations of the tales. Men "have a virtue to shape their life, amid the powers and chances of the world, beyond the music of the Ainur, which is fate to all things else..." Men, by definition, have free will in the Legendarium. "All things else" are constrained by fate, at least to the extent that the Music of the Ainur addresses their actions and sets forth fragments of their tales. In my view, the Music is not a complete and detailed history. but rather broad brush strokes regarding the world. Thus the waxing and waning of Elves, the nature of Morgoth and his minions, the design of Middle-Earth and more are set in stone Men are free of this influence... except to the extent they deal with those who are bound by fate. So it is indeed perilous for mortal Men to seek out and speak with the Elves and even more so for Men to interact with the Ainur. For Men to interact with Elves, the Ainur, perhaps even Dwarves and Ents, is to subject their actions to the fate directing the decisions and deeds of the other Speaking Races. Morgoth's curse bound Turin with fate, so that even when he exercised free will, his choices were tainted and fated to result in evil.

I suppose another way of saying this is that somehow Morgoth's curse is manifested through Turin's choices. His failure to rescue Finduilas is, then, part of his curse. It makes little sense, to me anyway, even to posit that, had he rescued Finduilas, his curse would still have found him. For the curse is (in part) that he failed to rescue Finduilas. One can easily imagine a lot of hypothetical worlds where Turin's lot is happier, had he made this choice or that choice differently. The curse is that he didn't make those choices differently.

Precisely! So why would Tolkien even bother to suggest that one of Turin's decisions, specifically whether or not to rescue Finduilas, would relieve him of his doom? This would be inconsistent with the nature of the curse itself, which twists Turin's decisions to evil. This is why I think that Tolkien, if he had assembled the hypothetical final version of the Children of Hurin, would not have included the version of Gwindor's last words that was included in the Silmarillion.