This looks like a fun alternative to classroom debates about whose intuitions are more justifiable (not that there's anything wrong with such debates!). I especially appreciate how the "character roll" to some extent gamifies Rawls' veil of ignorance. The explicit association of game characters with different theories (Nozick's, Parfit's, etc.) in your background document was also helpful.
Beyond Rawls' veil of ignorance and initial premises, are you generally able to pair this game with an additional discussion of the more specific political implications Rawls draws and the practical conclusions he arrives at? I would be curious to see whether playing the game might influence students to agree or disagree with Rawls' inferences.