Bryan Singer has one lying around spare.
Complete with episode titles lifted from The Second Coming.
And featuring a character called The 76th Distillation of Blue. Who you just know would be the breakout star.
Federation set in the year 3000 changes a bunch of stuff and doesn't change a bunch of other stuff, in order to have a familiar but more futuristic setting. Something I did when I pitched a Star Trek game set merely a century after TNG, as an excuse for explosions and phaser fights and aliens being kicked in the face.
Hey, I'm a Kirk baby. I want bright colours and running around and monsters and things that go boom. If Doctor Who can do it so can Star Trek.
(And as for The 76th Distillation of Blue, I was going to have Mr. N, a V'Ger-probe-style shifting column of light who speaks in humming tones, as the science officer. Deal with technobabble by literally making it a background hum.)