I admire your efforts, but there is absolutely no way that Hyrule Historia can be false. Why? Because It's an official document. No matter how many holes and inconsistencies you may find, the fact that it's official means that the contradictions found in-game don't matter at all. It can only be false if the developers have said so, and they have not as of yet. This is what "word of god" is.
Just because it's "official" it doesn't mean it's right. You'll probably say, it IS the right timeline because Nintendo said so, but think about three things:
1) When Nintendo makes a Zelda-game they try to make a good game not a game fitting in the timeline. Great example is the Four-Sword-series wich never had a clear place in the Zelda-Timeline. This timeline is probably just another theory that didn't exist when the games where made.
2) Nintendo likes to contradict themselves. Great example is the beginning of the timeline. They first said OoT was the first game. Later they said TMC and FS happened befor OoT. These is ok, because TMC and FS came out later then OoT. But shortly before the reales of SS they said OoT was the first game, with SS as a prequel. They already contradict themselfe, but even the so-called-official timeline contradicts their lates statement because it places SS, TMC AND FS before OoT. As you see they like to change their timeline and they probably do so in the futur. That's why I based my timeline on in-game facts not on anything they ever said.
3) (I'm not sure about this, so correct me if I'm wrong) The guy responsible for the book is Iwata. Iwata was first involved in OoT. OoX was developed by a third party (Capcom). And now look at the game in the "what-if"-timeline: ALttP, OoX, LA, LoZ, AoL. Do you notice something. All games Iwata wasn't involved. Maybe he gaved these games a lower rank because of this...who knows...