They could do a series of games. Like two or three if they felt particularly creative.
Set up: Triforce is not in the sacred realm but separate and scattered across Hyrule, but long time fans would know exactly where they are, in our three favorite recipients.
First game: Link's a kid in a small village, he's made aware that something is rotten in the state of Hyrule, exposes the big bad (probably Ganon or a
dragon of his in a final boss fight, but instead of Link beating him he runs off. Game ends, Link's a hero.
Second game: Link is a little older, he starts off say in Castle town training to be a knight because his skills were recognized in the last game, they all think the big bad is gone but then he comes back with reinforcements. Zelda sends him off on a series of quests to get items or sages or whatever is needed to defeat him. He does it, but it's not enough because he doesn't have the master sword. Game ends quite darkly, such as Ganon managing to take over Hyrule. Zelda and Link scatter because there's nothing they can do, Zelda tells Link he needs the master sword to defeat him.
Third game: Takes place a few years after the end of the second game and is on a quest to find the master sword and completes a series of tasks/dungeons to prove he is worthy of the master sword and then the triforce of courage. Zelda could be doing her own thing to obtain the right to wield the triforce of wisdom. Both go back to Hyrule, undo the evil he did to it, and then meet him for a final showdown. Butts are kicked, names taken, Ganon is sealed. Fin.
It doesn't have to be exactly like that, but it would be a way to see the same Link grow up and change through each game. I think the gamer would get a feeling like it takes a lot more to become a hero and could also join in seeing Link grow from a little village kid to a full fledged hero. SS proved they can make Link have a real personality without having to even let him talk, so it would be a lot of fun watching him change.