The typical sweet-spot for RPGs, 4-5 players, allows for individuals to pull against the collective centre of the story for a short time, before someone else pulls the collective centre in their direction. The whole story is a dynamic tension between the players, the GM and the rule set. In a 100+ player game, a single person trying to pull the story in a given direction finds it much harder to make significant impact due to the overwhelming inertia of so many other players. If a player wants to pull the story in a given direction, they need to gather a band of like minded companions to help. It's still possible, but it tends to take a group to derail things rather than an individual.
To link character develop and story into such a large framework means minimising a lot of the minutiae, otherwise there is simply too much to keep track of. I'm thinking of developing some story cards, each being a tiny objective, and once a player completes that objective they are given a new one. Each objective provides some minor bonus, it probably takes about half an hour to complete, and by the time six to eight have been resolved, a character will have told a specific story arc. Many of these story cards will require certain other objectives in the game to be met, some will be event drivers in themselves. It blows the word count, so maybe this is something to consider more carefully after Game Chef is over.