Actual Chinese cultural influences/aspects beyond the joke level Kung Fu stereotypes. Some reflection on what it means for their ancestors to be the enemies of the land they now call home, the ones they burned. Discussion over the value in preserving their Chinese culture versus allowing the Wasteland to change them. Do they mix (breed) with outsiders even?
Perhaps a subplot about restoring San Francisco's tram system.
Some sort of political subplot about the secrecy regarding the true nature of the Emperor and who actually is pulling the strings amongst the Shi
Establishment that the Shi make a living by fishing from the bay and selling to outsiders as a matter of trade. Fuse the Chinese culture with that of a working fishing community. Perhaps a light divide between the fishermen and those in the Steel Palace, the fishermen becoming more culturally distant from their Chinese heritage whilst those in the Steel Palace rigidly hold onto it, and those in the martial arts subculture are clinging onto to a fake, pastiche version of their culture. Which they're not truly aware of and hold in more reverence than the legitimate stuff. Which could either send a message about the arbitrary nature of the Steel Palace's "old world blues" and the folly of their pride in rigid cultural insulation, or as a warning to study and preserve your culture more carefully, dependent on the players perspective you could slap them down or embrace the kung fu as something once that wasn't part of them, but now it's as much Shi as any practice the Steel Palace mandates.
You could have the NCR as a wedge issue, whilst the Steel Palace dictates what goes, it's unwise to ignore the will of the people. The town is divided over the issue of NCR, and the Kung Fu plotline could be it's resolution. The two dojo leaders are both competing for victory, one is supportive of NCR and the other a Shi cultural preservationist. The players choice and victory in the tournament's would ultimately help decide the fate of the Shi. At least to some degree, maybe you'd have to help the Shi in numerous other ways to guarantee the incorporation into NCR