I've often wondered what the difference is between Christianity and Islam that the unsavory laws are, on the whole, interpreted so differently. Is it inherent in the differences between the Qur'an, which outlines a comprehensive system of organizing society, and the New Testament, which focuses more on the individual? Is it a result of Christianity's ambivalence towards the Law? Or is it just that biblical interpretation has been shaped by centuries of Western humanism?

Yes! Yes! Yes! It's so refreshing to hear someone else bring up this question, and I think you point to some of the most important causes. I don't claim to know all the reasons either.
A couple of other points. First, Judaism has been "interpreting" the law for a long time now, at least as long as Christianity has been around. So that may also figure in the history of Christianity, which unlike Islam started among Jews. Second, Islam has simply never had a century like the Reformation, or the Enlightenment; I don't think they had anything quite like the thirty years' war either.
Of course I completely agree with the point about non-Western Christianity; those societies are also more distant from the Reformation or Enlightenment. But I do think that there have been points in history when Christianity was more women-friendly than other popular religions (e.g. Mithraism did not seem to permit women at all).