In the non-political chat section of my alternate-history forum, there's a thread discussing how the different board members would've handled the Star Trek canon. It went from "what parts of the canon would you include" (the little-known animated series was discussed) to what aspects of the overall storyline would be included.
Here're my ideas:
*The Vulcans, having been traveling between the stars for centuries before humans developed warp travel, would have a substantial interstellar presence of their own. Them joining the Federation would be like the US joining Mexico or Costa Rica, depending on just how strong the humans get. The Federation would be various human worlds and less-advanced/powerful alien races, which would also explain why the starship crews are largely human.
*Hint that Surak was not such a wonderful person and the triumph of his philosophy was something more akin to totalitarian world conquest than the peaceful adoption of his ideas by all except the most irredeemably violent and deranged. Given how his ideas are as contrary to Vulcan nature as some extreme human philosophies are to our own, I imagine his ideas took a fair bit of violence and coercion to impose. The Romulans can be analogous to the survivors of the Alliance for Democracy fleeing the victorious Domination of the Draka to establish a free society at Alpha Centauri. The Time of Awakening, according to Star Trek canon, apparently featured severe warfare--this could be Surak or his successors imposing his ideas through conquest rather than the Vulcans being self-destructively violent until Surak calmed them. History is, after all, written by the victors.
This wouldn't make the Vulcans evil, mind you. Compare War Communism or Stalinism to glasnost, perestroika, or the reformed USSR the New Union Treaty would've created. The Vulcans could be embarrassed about the excesses of their ancestors or try to make excuses for them, but it's the Romulans who continue to hold grudges in the face of Vulcan efforts at reconciliation. The website had some really vindictive Polish nationalists who hate Germany and Russia who kept getting banned and sneaking back under new names, so I referred to the Romulans as "the Pole-Trolls IN SPAAAAACE..."
*Khan Noonien Singh's sleeper ship encountered some kind of space-time anomaly that catapulted them a fair distance from their intended destination. By the time of Star Trek: The Next Generation if not the original series, the elderly Khan is the ruler of the grandly-named "Great Khanate of the Milky Way" that, due to the small starting population and lack of an industrial base (at first), is actually a fairly small Augment polity with some primitive aliens in vassalage. A rival human state and fascistic-imperialistic foil for the democratic-socialist-ish Federation would be kind of cool story-wise.
*Speaking of democratic socialism, that the Federation was some kind of utopian state is essential for Roddenberry's vision, but it can be toned down a bit. I'd make the Federation a post-scarcity economy. If some form of socialism exists, it'll be the result of automation eliminating most jobs and the state eminent-domaining (socialism) or taxing (social democracy) the automated economy to provide the basics for the now-redundant population rather than letting everybody starve. There'd still be money (unlike canon) and still be jobs, but there'd be a guaranteed minimum income. Human nature is still human nature and "from each according to his abilities, to each according to his needs" is something that's rather difficult to make happen.
*About the Gorn, when I was a kid my uncle had a tabletop game called Strike Team Alpha whose storyline I really enjoyed even if actually playing it wasn't that fun. STA featured an antagonist race resembling evolved velociraptors called the T'Rana. Their polity came off as basically Imperial Japan IN SPAAACE--they were expansionist and predatory and promotion was achieved by killing and eating failing superiors (chronic assassinations by warlike junior officers that plagued pre-WWII Japan and of course in Star Trek itself there's "Klingon Promotion").
*The Klingons would stay the same, although I'd tone down their militarism some to avoid people wondering how they can have an advanced scientific and technological society if only being a warrior is respected. The plan is to avoid "Flanderization." The Borg would stay the same.
*On a micro note, the bridge crew and especially not the captain are not going to be going on away missions, at least routinely. I suggested having a Marine commander character leading most of those, but the user whose handle is RCAF Brat suggested Kirk have been in Fleet Special Operations (i.e. Section 31, although if Starfleet is the Navy their having something analogous to the Marines makes sense) before an injury forced his transfer. He still likes going groundside and does it as often as he can, much to the consternation of the other officers. At least this would "lampshade" how dumb it is to send half the bridge crew to a planet at any given time. Kirk's promotion to Admiral in the films could be more like him being "kicked upstairs" for recklessness and foolish behavior that has made him too popular with the Federation public to court-martial after his return from the Five Year Mission.
*On another micro note, make Spock a full Vulcan rather than a hybrid. Even though Vulcans are superficially humanlike, they'd be very different genetically. If humans can't breed with chimps, how can we possibly breed with beings from another planet?
Overall, you'd still have Roddenberry's optimistic vision of the future and human potential, but it'd be a bit more subtle and realistic than this.