Set Star Trek: Discovery after Star Trek: Voyager
So many of the complaints that we saw with Discovery would've been alleviated had they just set the show 15 years after the events of Voyager. With all the information that they collected, you'd totally be able to explain away concepts like the Spore Drive, the interactive hologram computers, and essentially the Discovery being the best ship ever.
You could also write far more interesting lore around the Klingons, who you could say left the public eye after the events of the Dominion War and underwent genetic alterations so they could once again become the threat of the Alpha and Beta Quadrants they once were; hence the new look. That would then allow you to do the entire Federation and Klingon war with these different-looking Klingons and not have to constantly explain or justify their appearances.
Not only does all this make more sense, but you can distance yourself from the idea that Spock had a sister that no one wanted him to have, while also attaching Michael Burnham to a different Starfleet family (if any at all). So instead of trying to ride the coattails of Spock, you could have Burnham be her own woman, allowing her to be more of a unique character without the burden of Spock's legacy now laying on her shoulders.