Yes, "social contract" is a restatement/clarification of what is meant by "his rational consensus". That is, his rational consensus (or final theory) was the social contract theory. You could restate the sentence as you have with i.e.
Something that "does not sit well" does not feel right, it bothers or irritates the conscience. You could also say that it does not fit. Think about a chair that has one leg shorter than the others. When you try to sit in it, it wobbles, and you become uncomfortable trying to stay seated in one position. In your particular example, you could substitute "does not agree well with", "does not align with", "is not consistent with" or "is contradicted by", though phrase might have subtle shifts of nuance.