Okay, so 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, the other two are not quite so easy.

[b][u]TRIANGLE OF POWER[/u][/b]
[b]Power[/b] - Used in calculating physical damage, the amount of weight the character can lift, and the distance the character can throw an object.
[b]Reflex[/b] - 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.
[b]Endurance[/b] - 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.

[b][u]TRIANGLE OF WISDOM[/u][/b]
[b]Wisdom[/b] - 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.
[b]Psyche[/b] - 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.
[b]Spirit[/b] - 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.

[b][u]TRIANGLE OF COURAGE[/u][/b]
[b]Courage[/b] - 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 [url=http://www.d20pfsrd.com/gamemastering/other-rules/hero-points]this link[/url] does a much better job than I would) are spent.
[b]Character[/b] - 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.
[b]Will[/b] - 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.