QC: Well, it's not like the piece totally vanishes. Link is unaware he has it until the last medallion is gathered, perhaps he hadn't earned the right to wield the piece until that happens, in which case it's found by someone else in the world.
That doesn't work, because the Triforce divides itself at the moment Ganondorf attempts to claim it. The Triforce picked Link for the Triforce of Courage. Quoting Zelda in OoT:
If the heart of the one who holds the sacred triangle has all three forces in balance, that one will gain the True Force to govern all. But, if that one's heart is not in balance, the Triforce will separate into three parts: Power, Wisdom and Courage. Only one part will remain for the one who touched the Triforce...the part representing the force that one most believes in. If that one seeks the True Force, that one must acquire the two lost parts. Those two parts will be held within others chosen by destiny, who will bear the Triforce mark on the backs of their hands.
This all happens before Link is sealed away for seven years, while he is still a child. If the Triforce of Courage did not choose Link at this point, then where did it go? How (and when) does Link end up with the Triforce of Courage?
QC: As for the second point, again this assumes Link always has the piece of courage. Zelda trains as Sheik expecting Link to return. If we go by the assumption this follows the ALTTP pathway, then Link's failure to return leads to war, the sacrificing of maidens to open up the holy realm in place of the hero. With the child viewpoint, Zelda returns to wage war with an army of desperate civilians, and the owners of those medallions being 6 of the wise men that seal Gannon away at the start of the story. That would leave either the King of Hyrule, or Zelda herself being the last, as the new Zelda is the last maiden to be sent to unlock Ganon and the Dark Realm. With the split occurring as an adult instead, then the war is delayed, Ganon having time to unlock the powers of his piece and building his own army, and probably making Zelda the last of the wise-men that seal him away. That's just a thought of course.
The above questions still apply, but there seems to be even more problems with this scenario.
First of all, the OoT-era Sacred Realm is opened by the time Link first claims the Master Sword (as a child). There are no Maidens to be sacrificed; the Maidens are descendents of the seven Sages used to seal Ganon in the Dark World and that hasn't happened yet.
Zelda's goal is to seal Ganondorf away so he can no longer do any harm. Her plan requires all seven Sages to participate in the sealing process, so Link
must be successful before revealing her identity has
any benefit - she cannot defeat him in any other way, and she knows this - that's why she doesn't reveal her identity until that has happened.
LttP tells us that in this branch, Ganon is sealed away. However, before that happens, he needs to complete the Triforce, because this is what causes the Sacred Realm to be corrupted into the Dark World (and LttP states that this had already happened when he becomes sealed away).
This alone seems to suggest that the seven Sages mentioned in LttP are different from the OoT sages, since Zelda is the seventh Sage. Zelda would somehow need to be captured by Ganondorf, have her piece of the Triforce taken from her, and then escape alive. Everything we've seen so far suggests that this isn't possible.