River figures out how to walk without her psychic powers. She leaves on the general sense of her surroundings, the precog and postcog, the projective telepathy and specific mind reads of her friends who she knows don't mind it. (Mal, Kaylee, Simon, Zoe, and Inara when she rejoins the crew - Jayne had mostly only been tolerating it as a cost of being part of Serenity's crew - and only the thoughts they don't mind her seeing. She and Mal toss increasingly bad jokes back and forth telepathically.) She gets better at the precog, figuring out how to make the feed more coherent and useful.
And when things start getting fixed proper -
River offers a bit of guidance on helping out with fixing the mess that is the Academy and its graduates, and on which Alliance officials are actually interested in negotiating in good faith. But, mostly...
It turns out she's really, really smart, and it's a wide multiverse out there with a lot of opportunities for a really smart girl - even if she doesn't leave her home neighborhood so she can keep her powers on. She doesn't bother with anything that calls for vetting, not right away, but she enjoys inventing and can do an awful lot of that just sitting in her bunk, and she finds she likes teaching other psychics how their powers work a weird amount. She starts putting together classes, mostly on a whim, and then more seriously when one of the frontier planets offers her space. (Being a folk hero for her opposition to the Alliance is actually kinda really weird.)
Mal rallies some of the Rim planets into seceding from the Alliance's official control. Other planets and blocs follow suit pretty quickly. River teases him about going into politics. Then, when Inara actually goes into politics, teases him about his crush being more popular than him.
Zoe backs him up, but mostly focuses on vacations with her husband.
Simon is almost as smart as River, and starts learning as much as he can about the state of the art in medicine across the multiverse. He, unlike River, appreciates the fact that governments ever exist and starts going through vetting for various healing magics.
Kaylee goes wide eyed over all the engine tech out there, of course.
Book goes back to ministry, once he's back alive.
Jayne drifts, for a while, not really happy with being someone's security and not really eager (or trustworthy) for anything requiring vetting. River dances around him a bit and then manages to prod him into extreme sports. He's good at it, so.
It's not really how River'd set up an ideal world, but... It's all pretty good, all the same.