@Thomas,
That is an interesting hope. I have two responses.
1. Modern science starts with a process. We have defined a system of determining (or defining) what is right and wrong. We then accept whatever the process yields. We didn't start with anything close to our modern understanding of science (Aristotle for example was completely wrong and Galileo and Darwin and Einstein were completely unimaginable before the process led there).
If you want a similar thing to ethics, it would be a process that would likely end up with different results then you are expecting. It seems like you are starting the wrong way around. You have ideas about ethics before you have defined this process and you are expecting the process to validate (rather than form) your ideas.
Before the modern scientific process was shown to be so desirable for developing cures and weapons and flying machines what was known as 'science' was really just a another name for 'religion'. Without the process of experimentation there is no difference.
2. There are plenty of human endeavors that we understand as being culturally specific. Linguistics is an interesting example... actually I think linguistics is a very good analog to morality, there are human tendencies that are manifest in very different ways (and no one ever classifies a human language as being incorrect).
Then there is art and music and religion. All of these built on human traits, but are manifest in very different ways between different cultures. Again no one looks at the art or musical ideas of any culture and decides they are 'incorrect'.
I think math and science are unique in that we understand ideas as 'correct' or 'incorrect' across cultural boundaries.