...my impression is that there is just enough variation to thwart this possibility.
I think you're probably right. Whatever it is, assuming "it" exists at all, would very likely be lost in the background noise. On the other hand, such a discovery would go a loooong way toward evidencing an objective morality. This might be one of those rare opportunities for theist and non-theist to work together - discovering an "objective morality" that applies across cultural and temporal boundaries would seem to be a major breakthrough in our understanding of our species.
Perchance to dream...