Rational Justice to Emotional Moral Judgments

Ethics are based in our emotions, but it seems that justice is based in our reason. This certainly suggests that morality and justice are in fact two quite different things. Yet, what are we to make of the fact that the "feeling of injustice" we have when we are cheated is in fact a feeling, an emotion? Is this in fact a sense that the person in question is acting immorally toward us?

Let us consider this:

Anyone who feels a sense of disgust at some activity will argue that the action in question is immoral. This is the basis of homophobia, for example. Yet, one can simultaneously experience this disgust and agree that homosexuals should, nevertheless, be treated equally under the law. However, I would have to wonder how long one would be able to feel such moralizing disgust once one is rationally persuaded against unjust treatment of homosexuals.

Might justice be reason's way in to persuade our moral sense?

I will also note that Haidt shows libertarians to show rather low emotional responses to ethical issues and to be more rational than most people. Might this explain why libertarians are so justice-centered in their thinking?