I’m also seriously leaning towards running Gothic Trek with my home-grown system, Triptych. For a warm-up, I generated a starting scenario using Rafael Chandler’s delicious “Starship From Hell” randomizer.
The ship is a Miranda class, the era is roughly Next Generation (though this is all Alternate Universe, so sticklers for detail are unwelcome.) Here’s a modified picture of the ship.
The idea is that the Federation is big, way bigger than we saw in the tv show or the movies. And at the edges of the Federation is not empty space, but other star empires or enclaves that have their own reasons not to join the Feds.
So, I work up a sector, note some of the conflicts and races at work there, and give my game group the equivalent of a Neutral Zone with some hostiles, allies, and more ambiguous factions.
Let a PC be captain of the ship, the rest important bridge crew, and do some gunboat diplomacy on the frontier. Along the way, deal with a vampiric star empire, werewolf assassins, perhaps a new expression of undeath in space, and whatever zany business I want. Mixed in with the tried and true exploration, diplomacy, morality, and expertise of traditional Trek.