The absolute best twist I've seen a few times plays on the 'Hunter of Artemis' vow. Someone wrote a story where Percy's affection for her isn't about breaking the vow at all—it triggers a forgotten clause. The love of a mortal can actually strengthen the vow, turning the Hunter into something more like a guardian spirit tied to that person's lineage. So her commitment deepens because of him, not in spite of him. It flips the whole conflict. Suddenly, the other Hunters aren't just tolerating a weird exception; they're witnessing a rare, sacred event.
Another favorite is when the twist isn't in their relationship, but in Percy's nature. One fic had him slowly manifesting powers that weren't Poseidon's, but more primordial, tied to the wild places Artemis protects. He starts understanding her on a level even she doesn't expect, speaking to ancient forests and calming celestial winds. It makes their connection feel destined in a way that isn't cheesy, but deeply rooted in the mythos.
Less popular but totally gripping are the darker turns. I read one where the 'Percy' she falls for is actually a compelling illusion woven by a forgotten god of obsession, using Percy's image to corrupt her vow from within. The real Percy has to team up with a suspicious Annabeth to expose it, creating this awful, poignant tension where the Hunter is fighting to save a love that was never real.