While trying to brainstorm about these Ability Scores, I came up with some ideas, and I'll list their current possible functions below. While the Triangle of Power is practically a no-brainer (being a near copy-paste of the traditional D&D Physical stats), the other two Triangles are not quite so easy.

TRIANGLE OF POWER
Power - Used in calculating physical damage, the amount of weight the character can lift, and the distance the character can throw an object.
Reflex - Used when determining Initiative, when attempting to land a hit (particularly with ranged weapons like bows), and in determining a character's ability to avoid attacks.
Endurance - Used for determining a character's Heart and Stamina, as well as the character's ability to resist poisons relating to the Triangle of Power, Combat Maneuvers, and the like.

TRIANGLE OF WISDOM
Wisdom - High Wisdom scores increase the number of Spells known for spellcasters of all kinds (also used by Alchemists and Psychics [Zelda had some Psychic abilities, like telepathic communication, so please do not try the "Psychic has no place" argument on me] for their Extracts and Powers in the same way); Wisdom also is used when calculating magical damage, and is also used for a number of Skills.
Psyche - High Psyche scores increase the number of Languages a character knows, as well as serving as the base Ability Score for Knowledge-based Skills; Psyche is also used when calculating damage for Psychic Powers.
Spirit - Used for determining a character's Magic Points (Used for Spells, Spell-Like Abilities, Extracts, and Psychic Powers), and also Heart Points for Undead beings; Spirit also is used for resisting poisons relating to the Triangle of Wisdom, as well as harmful Spells.

TRIANGLE OF COURAGE
Courage - Used for resisting intimidation and fear effects, and also for granting bonuses when Hero Points (I could spend forever trying to explain this to those who are unfamiliar, but I feel this link does a much better job than I would) are spent.
Character - Used when trying to influence others, hide one's presence, lead anything from a small band of adventurers to a grand army, and can even increase the number of Hero Points gained.
Will - Used when resisting poisons relating to the Triangle of Courage, as well as harmful Psychic Powers; Will can also be used to resist non-intimidation or -fear effects from Character-related effects.

In addition, I'm considering having Feats which, at a cost (Likely in Stamina or perhaps even Heart Points) and under the correct circumstances (a.k.a. a crapton of prerequisites because it's kinda OP), allow you to temporarily use the Ability Scores from one Triangle in place of the scores from another Triangle, in which Courage, Wisdom, and Power would be interchangeable, likewise for Reflex, Psyche, and Character, and again for Endurance, Spirit, and Will.

Next is what I am calling the Trinity of Vitality (an element I would like to implement, if deemed wise): Heart, Magic, and Stamina. Heart is another name for Hit Points, the name change simply for aesthetic purposes to fit the world better, and is determined by Heart Dice and Endurance, just as Hit Points are traditionally determined by Hit Dice and Constitution. Magic is where things start getting tricky, as rather than spellcasters getting a set number of Spells per Day, each Spell (or Spell-Like ability--meaning even non-spellcasters will still have a Magic Meter) will have a Magic cost, and when a character's Magic Points reach 0, they can no longer cast Spells until they can replenish their Magic. Magic would be determined by Magic Dice (akin to Hit Dice) and likely Spirit (if not Spirit, then Wisdom). Lastly, Stamina is consumed by strenuous activities similarly to Magic being consumed by Spells. However, Stamina would automatically recover over time for each round the character is not doing strenuous activity or in combat. When all of a character's Stamina has been depleted, they are overtaken with fatigue: they can only move at half their normal speed, and cannot partake in combat or strenuous activity until their stamina is restored, which would now recover at a quarter of the rate it normally would. Overexerting a character's Stamina would result in the difference being subtracted from their Heart Points. Like Heart, Stamina would be determined through Stamina Dice and Endurance.

When a character comes in contact with the full Triforce without earning it, or without the perfect balance and purity of character with which to obtain it, it shatters into three, Power, Wisdom, and Courage. Since there's not always going to be a Link, Ganon, and Zelda around to possess the pieces, there has to be a way to distribute the Triforce during such times. The idea, to keep things perfectly fair, is that when a character touches the complete Triforce--be it a player or an NPC--the "Goddesses" (a.k.a. the GM) would then evaluate the characters of the game. Then, based on the stat totals in each Triangle, the Triforce is scattered with the appropriate pieces given to the appropriate characters. A GM might simply place the Triforce off-limits, but for campaigns which do have it available, the game needs an unbiased method with which to distribute the Triforce.

This is not to say I cannot simplify it to less than 9 stats, but simply that each piece of the Triforce needs to be equally and properly represented in whatever stat system I use, so that order and fairness can be upheld in an event such as described above.