A lot of what I have to say about this theory has already been said, so I'll try my best not to repeat too much.
It seems that this theory somewhat relies on the Hero of Winds being descended from the Hero of Time, since that is the explanation for the Hero of Time's motivation to return to the Adult Timeline as well as for pretty much everything to do with the apparant moving of the Master Sword. However, in-game quotations from
The Wind Waker, which Zurriel brought up, prove this to be false.
Jabun: If you have sought me out...it must mean
you have found the Hero of Time,
does it not?
King of Red Lions: Unfortunately, that is not so.
Jabun: Then for what purpose have you come to
see me?
King of Red Lions: The one I have brought with me has no
connection to the legendary one.
And yet I sense great promise in the
courage that this one possesses.
As Blue pointed out, The King of Red Lions already knew that Tetra was the descendant of Princess Zelda at this point:
Jabun: Tell me, Hyrule King...
Have you learned the whereabouts of the
one who carries on the bloodline of the
princess, Zelda?
King of Red Lions: ...I believe I have
It's possible he came to this conclusion due to Tetra's possession of his Gossip Stone but that seems like pretty weak evidence to trust when dealing with the greatest evil the world has ever known. After all, he goes to the trouble of making Link prove himself to the Gods themselves before he explains what's going on to him. How The King of Red Lions knew Tetra was a descendant of Zelda is unclear, but if he could identify her lineage then surely he could identify Link's lineage as well. He outright states that Link in
The Wind Waker has no connection to the Hero of Time. I take in-game information as the highest source of canon, so this, to me, is fact as far as the series is concerned. The Hero of Winds is not a descendant of the Hero of Time.
The HC in TWW couldn't have been built over the ToT, because neither were on a cliffside of a giant body of water at the time the HoT left the AT... It is more than likely that someone of the bloodline or the HoT himself moved it; probably for better protection from corrupt hands looking to release Ganon.
This is another key point in the theory, that the Master Sword is in a new location and only the Hero of Time could have moved it. Most of what I have to say has been said, chiefly that "wield" does not mean "hold" and that it is never stated that the sword can only be used by the Hero of Time and his desecndants (
A Link to the Past states that, "one who was pure of heart and strong of body could wield it."). The Hyrule Historia itself proves that other people not connected to the Hero of Time can move it. It was you yourself who brought up that Zelda is the one who returned the Sword after sending the Hero of Time back.
A case can be made in favour of the Sword remaining in the same location between games. We know Zelda returned it to its pedestal in the Temple of Time and that the next time it appears on the Adult Timeline it is in the basement of Hyrule Castle. This suggests the blade was moved. But in the Adult Timeline, Hyrule Castle and the surrounding town was utterly destroyed and a huge crater was left in its place. Clearly, the castle was rebuilt at some point. Castles are built for defence, nothing more. They are structures designed to be defended, to keep kings safe. Building what is nothing more than a fancy fort directly on top of the Master Sword would be the easiest, most direct, and, to a mostly medieval society, the sensible thing to do in order to protect it. All of the turmoil that had swept Hyrule for seven years was caused by someone getting access to the sword, and its placement in
The Wind Waker seems to be focused around denying access to all who are not permitted.
You are stating that this could not be the case based on the local geography alone. It's true that the large body of water did not exist during
Ocarina of Time and the effects of The Great Flood and erosion and the time-frame this all took place in could be debated at great length with no result. We could discuss how the town that surrounded the castle is nowhere in sight, how the immediate landscape is far more hilly than the relatively flat expanse of Hyrule Field, or that humans are more than capable of creating their own lakes and rivers, especially when they have access to explosives. Blue said it best when he said that "Geography is never a great place to look to when it comes to theory." It's just too inconsistent and has little meaning in
Zelda. The physical changes to the castle and the surrounding area are not enough to dismiss the possibility that the sword remained in the same location between
Ocarina of Time and
The Wind Waker.
My point here is that it can be argued that the Sword can be moved, and indeed wielded, by someone with no connection to the Hero of Time, and that it can also be argued that the Sword never moved at all but new buildings were built around it. I'm not saying you are wrong, just pointing out that dismissing one explanation does not prove the other.
In TWW, TKoRL told the HoW that before the HoT departed, he shattered the ToC into 8 pieces, however, he did not before he returned to the past, as we can see at the end of OoT. If he broke it by leaving, we don't see that as well.
It is still said that The Hero of Time shattered it before he left.
It is never stated at any point that the Hero of Time personally shattered the Triforce of Courage. The actual quotation is as follows:
When the Hero of Time was called to
embark on another journey and left the
land of Hyrule, he was separated from the
elements that made him a hero.
It is said that at that time, the Triforce of
Courage was split into eight shards and
hidden throughout the land.
Even I do not know where they rest, but
this much I do know: they lie hidden
somewhere in this Great Sea.
This is vague at best, yes, and it is clear from The King of Red Lions' wording that this is another event that has passed into legend and the exact details are lost to history. What he
says is that the Hero of Time left Hyrule, and then that the Triforce of Courage was split into eight shards. These are stated as two separate events, so while we don't get any details we do get a sense that they are not connected as directly as you suggest.
There are other explanations for this split. For example, we know that the Triforce has some kind of sentience because it senses the good or evil in a person's heart ("The resting place of the sacred triangle, the Sacred Realm, is a mirror that reflects what is in the heart...the heart of one who enters it... If an evil heart, the Realm will become full of evil; if pure, the Realm will become a paradise." - Sheik,
Ocarina of Time) and it even talks to Link in
A Link to the Past. For this reason it is possible that the Triforce of Courage split
itself, waiting for another Hero chosen by the Gods to claim it.
This is just one possibility. Another is that the Gods themselves split it for the same reason. Another still would be that Princess Zelda split it, given the precedent for the Royal Family hiding the Triforce given in
Adventure of Link. The point is there are numerous possibilities as to why and how the Triforce of Courage split and each can be backed up with supporting evidence. That does not make any of them true. We simply don't know enough about this split to say for certain either way. Again, I'm not saying you are wrong about the Hero of Time splitting it, just that you need to provide clear and solid evidence to back that statement up.
I can see that you've worked on this theory a lot and are drawing on canonical sources of evidence for most of your statements, so for that, kudos. It's good to see a theory that came out of logic and reasoning rather than liking the idea of something and pretending it is true, even in the face of solid contradictory evidence. That's the difference between theory and fanfiction. However, I personally don't agree with this theory because there are too many "maybes". The Hero of Time
might have split the Triforce of Courage, but the theory doesn't prove it. The Master Sword
might have been moved somewhere else, but the theory doesn't prove it. Theory also doesn't prove that Link could have travelled between timelines. For me the biggest point against it is that we know the Hero of Winds is not connected to the Hero of Time.
Despite that, this has been an interesting thread to read and, whether I agree with the theory or not, it got me thinking about things I otherwise hadn't thought about (like the possibility that The King of Red Lions knew the truth about Tetra via the Gossip Stone) and that is always good thing.