Captain Natalie Portman
She would have been twenty years old at the time. Interesting move, I like it. Would have brought in the all important 18 - 25 youth demographic.
It would be lighter in tone
I like this, not to the point of being a comedy, but put some humor into the fact none of them have a clue about what they're doing out there.
Oh and shift it forward ten years, just after the Romulan Wars and the formation of the Federation.
I'd go the other direction multiple decades. Consider this change, the warp drive is like the jet engine. First used on aircraft in 1939, three decades later they are everywhere. Military, commercial and private.
It's the same way with the warp drive (first flight 2063), by the year 2090 Humanity is exploding outward from Earth, very haphazard, colonies, trade with aliens, private exploration. A lot of alien toes are getting stepped on, the surrounding civilizations have never seen expansion like this before. And pirates are hitting Human ships.
Starfleet is formed in 2110 to attempt to bring order to this building chaos.
Not a universally popular idea with all Humans. Some members nations of United Earth have already formed their own armed fleets to protect their colonies and trade corridors. The New United Nations has a small armed fleet. As do some private corporations.
The show's first season is set in 2120
Mandy Patinkin as Phlox
Phlox is one of the characters I'd leave alone, casting and backstory. I'd keep Trip and Hoshi too. But I would keep her first season Hoshi for the entire run.