Joking aside, from a visual perspective I would have preferred what they did in "In A Mirror Darkly" 1 and 2, keeping the original TOS look but enhancing it to be on par with modern standards. So, we have 1701 digitally remastered outside and inside, "modern" warp effect, add more phaser banks ( blue!) and visible torpedo launchers. Uniforms are the same as in XI. More TOS looking ship classes. I'll consider characters and plot later.
yep this sounds like a good start to me!
As much as I love TOS and the original Enterprise, it would not have gone down well for a general audience.
This is a simple truth that must be faced.
Nothing we say or do will change the layman's reactions.
Oh, please. The Layman's reactions showed they couldn't even tell the difference between the new Enterprise and the one from TOS. The old one properly pushed up with modern technologies and detail, would have worked just as well.
Similarly, that everyone is all happy about the uniforms that essentially exactly the same as the original, once again showed, the audience would have been just fine with it.
Now, how would I have done it. First off, indeed the outside of the ship would have been the same as the original TOS, with a few improved detail here and there - that is, if the Enterprise is even in it. The insides would have gotten an upgrade, but have kept the same feel as the original - that is, it would seem like a fully functional modern bridge, and yet at the same time, have enough of the color scheme of the old, that you could squint and believe it's the same ship.
There would be no time travel, period.
If I deal with the Kobayashi Maru, Kirk would have done it after lots of times trying it, and he'd be frustrated, unwilling to give up. Cheating on it, he'd do at the prompting of Gary Mitchell; and it wouldn't be a simple virus sent to some chick (talk about bad computer science.) He'd lead a group of cadets, after convincing them with arguments and his innate leadership qualities, that they should work together to beat the simulations - one more reason why he'd be commended later on. He also wouldn't sit through the simulation like an a-hole, indeed he'd be the nerd and geek he's said to be in the first years of his carreer. The he'd take the simulation, even the reprogrammed one seriously, and even reprogrammed the simulation wouldn't be easy.
The story would deal with Kirk's time as a Lieutenant at the Academy, both teaching and going through the command program - of which teaching is part of. He'd take one class of cadets out on a training mission that would go to shit. McCoy would be part of it, as would be Mitchell. He'd have to deal with Orion pirates and Klingons. The ship that would be the vessel for the cadets would be the Enterprise under Captain Pike, Number One and science officer Spock, and would show Spock's and Kirk's first working together - which doesn't actually go to well. Spock isn't entirely impressed with Kirk. It'll also show Kirk and Pike's loose friendship forming.
In the last scene, "a certain number of years later" would have Kirk taking over the Enterprise from Pike, who hands it over to Kirk with pleasure.
The story would be partially political intrigue and partially action; weaving a multi-layered story.