There's no convincing way you can make Dax leaving her entire life to follow some random man she and the audience literally just met genuinely dramatic in the span of around half an hour, especially when the actors have negligible chemistry at best. The better-but-still-not-great revision would simply be to reverse the conflict and have the potential love-interest want to leave the planet with them. That would be pretty pedestrian Trek writing - having an alien that wants to go with the crew but ultimately rejects it because reasons isn't breaking new ground exactly - and it also takes away the dramatic focus on Dax as a character to be more about the guest star. Still, it doesn't contort Dax as a character with such a contrived and out-of-character conflict - seriously, she's acting like Crusher in Sub Rosa only without a fart ghost brain-washing her - and she'd still be the focal main character in this.

Then there's the Brigadoon concept, which really feels like a premise for a bland early TNG episode. There's just not much you can do with that creatively to make it particularly interesting compared to something like the town from the musical because it's not really functionally different than any given planet we've seen before and never returned to, and likewise for Dax whether the planet phases away or not if she left DS9 to go literally anywhere else it would mean the same thing to us. If I were to make an alternative suggestion it would be to make it an early Human colony that got engulfed in a time-space anomaly thingy - or maybe ancient alien super-tech to make it easier - and now bounces around the universe like a TARDIS, that would give us some kind of context beyond your conventional weirdo planet-plot. These would be the early pioneers of interstellar colonization and thus you'd get similar anachronisms to what you're homaging relative to the show's setting at least.