First, I would stick to small-time actors to play the main roles. Not that these people are not good at what they do, but that I want them to make their roles as different from the Prime Timeline characters as possible, from the Kelvin Timeline. Secondly...no Wesley Crushed as a principle character. In fact, I would have fewer principle characters on screen, with the rest having cameos. At least, initially. Third, I would revamp the aliens a bit. Make them less human-looking. I'd give Deanna Troi an identifying physical feature that (like some eye color that humans clearly cannot naturally produce). Finally, I would make technology border on "magic". Meaning, it is still familiar Tec, but it is so advanced that 21st century humans would have difficulty decipher it. Human beings of the 24th century would be more advanced physically (slightly stronger, healthier and can live twice as long, but are still in near-perfect health), but are not too advanced emotionally (still have a ways to go), but better off than 21st century humans.
Food for thought...
