Problems a-la "didn't ask for it" and "less excited about being stuck" are artificially exaggerated. These problems are already exist on another colony ship, which we mistakenly call the planet Earth. Nobody on the Earth "did ask" or "free to escape". Therefore, some minority constantly commit suicide because they didn't ask to be born, because they didn't managed to find friends or meaningful activities, or whatever. Yes, it is a problem with such people. This problem should be addressed to psychologists.
It's not the same at all. Here (well, in the western world at least) you're free to do whatever you want, build whatever you want, live the way you want. Sure, some people can't fit in but that's very different from entire generations growing up in a totalitarian environment where all key choices have already been made for them by their ancestors and they must stay on course charted for them by someone else.
I believe that this problem could be bigger on Colony ship, compare it to Earth. But it would never be game breaking. Because game state can be broken by motivated people, those who already accepted that they are born at certain place in certain time. "didn't ask for it" people do not make mutiny, because it has no meaning for it - after mutiny they still cannot step out from the board, but commit suicide. However, those, who accepted their being on ship, can start the mutiny, but not with "didn't ask for it" excuse. I see that problem "didn't ask for it" is not something inherent to Colony Ship only. It is common thing for the everyday life on Earth and already has approaches to reduce it to accepted level. Here is no place to explore and introduce something new.
Look up 'revolution' when you have a moment.
It is the same, and I will show how it is the same, but you need to stop talking with slogans and get out of Earth-centric thinking, since you are doing Colony Ship game.
Slogans "you're free to do whatever you want, build whatever you want, live the way you want" hide away that you already assumed that I am NOT FREE to do
1) Something what is not bound to Earth environment, kind of "romance a black minotaur mutant or alien".
2) Something what is not bound to human capabilities, kind of "let everybody disappears, and I will be the only one on the Earth. May be I will take my girlfriend too."
3) Something what is not bound to traditions, laws and moral, kind of "let me have seven wives, and I will exploit them for my pleasures openly".
I mean, that not "some people can't fit", but half of civilized humankind can fit. All western men lives with urgent need to fuck everything moving, but they never started a revolution on such premise. Instead, they are trying to fit "traditions, laws and moral" and use alternative, non-revolutionary approaches to satisfy their needs. Western men jerks, fuck whores, lovers and other objects for centuries without starting any revolution. Here I want to hear that it is not true that all men want have seven wives, and exploit them for their pleasures. I knew, "sure, some people can't fit" and two wifes is enough for them. Does it your choice to have one wife? When it was done for you? Why you are still stay on course charted for you by someone else? How did you manage to fit it?
In addition, nobody started revolution because of lack of minotaures, aliens or because of other people existence.
I provided you with these examples, because I see that it is you, who have to look up "revolution". All revolutions have economically bounded reasons. Revolutions starts because of urgent need to redistribute power, which arisen from new resources held by new group or a kind. People itself, their dreams, upsets and misery can live forever without revolution. If you are not going to show pre-revolution state of power and resource distribution, followed by new group of new resource holders aroused and urging new way of power distribution on the ship then, please, never touch the word "revolution", stick with "mutiny". Revolutions have fundamental change paired with an open break with the previous state. Moreover, Colony Ship is the last place where you can find possibility for this.
Anyway, I would ask you to apply your earthlike way of thinking about "you're free to do whatever you want, build whatever you want, live the way you want" the same way to the Colony Ship. You should not allow colonist to dream about non-ship environment, as if you striped away non-Earth environment from Earthman freedoms. You should not allow colonist dream about living on Earth since in out of their capabilities to bring themselves to Earth. You should not allow colonists start revolution because they just want to have something. Let them fit their environment, let them fill all shitholes like Eskimos live in Alaska and even do not migrate to Florida for "you're free to do whatever you want, build whatever you want, live the way you want" premise.
If you want to explore people living on Colony Ship then let these people to fit its environment first, fill all niches imaginable; find alternative ways to satisfy their needs. Exploration of fitting their environment should go as deep as you could find examples on Earth. Otherwise, “Revolution!” is just buzzword for getting lulz because it cool to have revolutions and guns.