The game looks interesting! Good luck with development. Will it be available on Steam (or GoG)?
I don't have too many ideas, but just to get the thread started:
1. "
Woman or Tiger"-style series of events - you, as a leader, have sparse information about what happened, and have to use logic to figure it out. (for example: Johnny was shot and there's three people suspected. He was shot with a pistol and two of them have pistols, but both of them have alibis; one of them must be lying and the other must be telling the truth, BUT... so on)
2. If there are any young people on board, they're sure to be restless and disobedient (more than adults, at least), and banding together to egg themselves on. Confronted with growing unrest between them and the threat of a forming gang, you have to decide what to do - split them up among different jobs? Punish them to deterr them, risking justifying their anger and making yourself look like a bad gu, and the punished - martyrs in the eyes of the other disgruntled kids? Use their closeness to give them a job that involves communication, but risk their inexperience and impatience sabotaging it, taking precious resources?
3. A search party is missing, and the probability of them returning are slim. Send a search party for the search party? (spoiler: they're all dead anyway, but your decision has an impact on your people's views of you.)
I might add more as I think of them!