I think you are on to something, but I'm not seeing the connections yet. For starters, "morally correct" is another term that can be defined in different ways. So you really lost me.
You ended your piece with the words: "justice, truth, and humanity." I think these are terms you should apply to your three situations.
Let's use your first example. Truth: most people who exhibit sexual desires different than the majority heterosexuals are just hardwired differently in a biological sense. Justice: they should not be judged differently because of their hardwiring. Humanity: they deserve similar opportunites and freedoms.
I think that with Truth, Justice, Humanity, you remove a lot more ambiguities than "moral".