All of your examples dealing with morality take a consequentialist stance with regard to ethics. I don't think that anyone has ever doubted that science might be relevant in computing the expected consequences of actions. So, I don't think you are saying anything fundamentally new here by applying science to pairs of ethical maxims rather than to one at a time.

But a lot of people are not consequentialists - they are deontologists (i.e. believers in moral duties). That duties may be in conflict on occasion has also been known for a long time - I'm told this theme was common in Greek tragedy. I'm curious as to whether and how your methodology can find a toehold for science in a duty-based account of morality.

For example:

• Everyone has a duty not to masturbate.
• Every married person has a duty not to commit adultery.

Where is the conflict, even if science is brought in?