One idea for a story that I have thought about was one based around a faction (or at least a localized version of one) based around survivalists who were also martial artists around the San Francisco Bay Area. The long story short is this faction rose as a group of benevolent mercenaries that are similar to the Followers, but not anarchistic. And after the events of Fallout 2, the Shi works with them to nation build to counter the influence of the NCR and remain independent.
As for what the society has become, I would make it to be more a foil to the NCR. Instead of being a replication of the pre war US down to all its corruption, mismanagement, individualism and sham of a democracy, this society would be a quasi theocracy, that's more collectivistic, planned and a society that is anti corruption. This society would have spent the time after the end of Fallout 2 trying to build itself up to being on par with the NCR. So between 2250 and 2275 people in this new country have worked like the US during World War 2 and used the surplus resources to further advance themselves.
The collectivism kicks in when it comes to the society's general ethos, you better yourself through your work, which betters the country which entitles you to social benefits. Benefits like you getting housing, health care, education and other social services as a reward. The downside would be prior to 2275, most people worked 12 hour days where basically anything that could run 24/7 more or less did. This society also tends to focus more on spying and intelligence gathering to compensate for the numbers difference.
The juxtaposition with the NCR would be the main story taking place after the Second Battle of Hoover Dam. The NCR lost and its going through a period of social upheaval. (For the sake of the story, we're going with the Independent or House endings rather than the Legion one). The Battle either cuts the NCR off from water and power from Hoover Dam or the prices that House charges causes inflation in the NCR, which kicks off an economic and social collapse in the heartland of the NCR. Which causes the NCR to pull their military from basically everywhere north of Bakersfield except a few outpost. Raiders and other criminal elements rise in the vacuum and the northern parts of the NCR start to balkanize. The NCR, for what it's worth, still claims the north but can't enforce it at this point.
The Shi country is having to deal with the fallout from the rise of the warlords along their borders and them attacking towns and villages along the border. The story would center around you infiltrating the various warlords, bringing intelligence back to your people, setting up resistance networks among the occupied people and other shenanigans. You'd be one of many people sent in to set up an intelligence network, so you are a part of an operation rather than the second coming here to save the world. Also, its not like a conflict involving warlords in California would have Earth shattering repercussions like the making of artificial people or whatever.
Other miscellaneous things involved in the story would be this new nation would be them having a policy of only getting involved in wars for self defense and not imperialism, but they have fought and expanded their territory under this policy. This society also uses its social services as a machine of propagating and building a new culture. One that more or less fills you life with education, work and other activities basically from the age of 5 to 21. So by ~2281 most of the population has been raised in this culture. Not to mention the culture is also a bit "manufactured". Smaller social conflicts would be around a society that has achieved a level of development that was promised when the nation was formed and that people have been sacrificing for an has only slowly been fulfilled. There would be anxiety around society changing, but now having to face a crisis and the public might not having the appetite to absorb and develop another swath of territory, coupled with a political class that doesn't want to change too quickly, but does want more territory....for self defense of course.
This story also deals with some of the threads that were pulled on during New Vegas, like the NCR not being in the best of shape after Tandi left office and going through decades of expansion and embracing corporate corruption. It would also show that House, powerful as he might be, isn't infallible. His actions being the thing that directly kicks off the troubles in the NCR's heartland and hurts himself in the process by cutting off that "society of consumers" from New Vegas.
