Morality is simply one or more groups' discourses put into an ethical sphere and labelled as such. The idea that there is one universal morality is deeply flawed (unless of course we add religion into the equation, but seeing as you have discounted that from the outset we do not need to cover it) because morality has changed so much as each society and social group's discourse has been changed. As the discourse changes so too does the morality, which in turn will affect all subsequent discourse and so on. I think you would be hard-pressed to find too many academics who disagree with this general statement, though they would probably frame it differently or along their own discursive lines (or that has been my experience at least).

Now, the entire field of science is based in Modernity, which is itself simply a broader social discourse that is commonly agreed on by most (if not all) of the major powerful discourses that most people ascribe to. As such looking to apply anything even resembling the scientific method to morality will only find what is considered the most moral thing from the point of view of a Modern society. As society continues to develop away from the search for an 'objective' truth (as it already is) and moves towards a Postmodern society or something resembling it, the morality that is discovered by this scientific method would be proven to be more and more vaunted as other, minor, discourses are examined and given voice and the major discourses change in relation to these and each other. Thus discourses would change and, again, so too would morality. This would only pick up pace as discourse pluralises, as it has for much of the last two centuries. So, ultimately, the search for an objective morality would suffer from general human advancement and would find itself quickly outdated and vaunted, a relic of a Modern age.

2 cents.