The problem with the sword-girl theory is that, if the sword-girl is supposed to be a major part of the story, it would mean that Link would have to get or learn something important about the Master Sword atleast 1/3 into the game. Link has never gotten the Master Sword that early, and the sword-girl can't play a big enough part in the game if she comes late. The only possible way I can see this working is if Link doesn't actually get the Master Sword and "sword-girl" early in the game, but that a major part of the story line involves Link trying to get in contact with this spirit. Which would mean that the conflict revolves around her.
Also, the notion of sword-girl is only relevant to the TP version of the Master Sword, because other versions don't have the same features. Which would mean that if this is true then this game must happen after TP, which means that G-Dorf can't be the main villain.
Also, where does "Termina is the Mirror of Hyrule" come from? I've never heard of such a thing.
ALSO, if the place where this story take splace IS Termina, should we expect to see some of the same land features as in MM? The TP version of Hyrule wasn't consistent with the OoT version, so it's likely that if Termina is the land, then there may be some big differences in geography.
ALSO, and most importantly, a sword-girl storyline wouldn't be consistent with TP, because Link had the Master Sword for a good while and never had to encounter a spirit. If Link all of a sudden shows up in a new situation, already has the Master Sword, and the spirit decides to help him for no good reason, then we'd have to wonder where the spirit was in TP. Which brings me back to the notion a good bit of time will be spent trying to get in contact with the spirit via rescue or some complicated set of tasks in which Link must gather something in order to awaken the spirit. I'm leaning more toward the former because if the story were to take place in Termina, it would make no sense for there to be a preset way for Link to channel the spirit of the sword in a parallel universe to the actual place where the sword was made, in a universe where the sword doesn't exist. So the only way I can see the sword girl thing playing out in Termina, after TP, would be if something (probably the main conflict) causes the Master sword to lose the spirit, and Link having to regain it. This would also mean that whoever the main villain knows about Link and the Master Sword, and has reason to fear it. Yadayada yada, there's tons of more speculations that I'm thinking of, and I just realized that it'd be stupid for me to try to write them all.
I'm kinda banking on an alternate timeline.