The Child Timeline and the Adult Timeline are completely contradictory.I still believe that the two 'Hero is triumphant' timelines both happen. I never read Hyrule Historia cover to cover (I read parts of it with a friend; I just read the relevant text that you quoted online, however), but from what I read, what you said, and what I know from games released after the publication of it, there are a lot of unexplained tidbits (from older AND newer games) that, if you assume that the Child and Adult timelines are one and the same, make things completely clear.
The only way that this could happen is if, after Ganon is defeated in the future, Link has the option of choosing to prevent the Master Sword from being pulled and warning the Royal Family, or going back and properly living his childhood in the age and time he came from, and in both cases, the events of Majora's Mask happen, but Hyrule is never flooded in the second case, since Ganondorf still has entered the Sacred Realm.
Also, I'm not trying to debunk Hyrule Historia; I'm just saying that it WAS only written to appease fans, and rushed ahead of the release of Breath of the Wild's initially anticipated release (probably so that they wouldn't have to rewrite half the book to account for it). As a result, one might want to take some or all lore from it with a grain of salt.
In the Adult Timeline, Ganondorf is sealed by the sages. After escaping, it is explicitly stated there's no hero, so Hyrule is flooded. Hyrule is later washed away completely by the King's wish, and Ganondorf is stabbed in the head and killed. There's no room in-between those events for the events of Twilight Princess to occur.
In the Child Timeline, Ganondorf is imprisoned in the Twilight Realm instead, escapes, and the Hero of Twilight stabs him in the belly and kills him. There's also no flood.
We know for a fact that it's the same Ganondorf in both games, but you're saying he died two different ways in a singular timeline?











