Your criticism is specious because the distinction that exists between neurology and genetics is not relevant to the discussion.
Let's simplify this by going back to a basic question.
Is morality anything more than evolutionary advantage?
You specifically said random mutation. Thoughts are manifestly not random, and not the product of mutation. Human morality is a product of human thought and cultural development, irrespective of whether or not humans evolved, and irrespective of whether that evolution resulted from random mutation plus selection.
Is morality anything more than evolutionary advantage?
Of course! It's like any other product of the human intellect, like a song, or a play, or a screwdriver, or a gun, or a model made from Play-Doh. These things serve human purposes, which may or may not pertain to human survival.
As it turns out, moral systems do help us to survive, but they clearly have other purposes besides.
I can think of several instances where morality is to the detriment of evolutionary advantage. I've already mentioned one man, one woman. Then there's Christ, obviously a great man, a leader, someone who is extremely valuable to society, but he could have lived and reproduced had he not done the moral thing of trying to save everyone. Is becoming a priest moral? That definitely hurts reproduction. A man in WWII harbors Jews from the Nazis, an extremely moral act, and is executed for it. The immoral act of initially reporting the Jews would have allowed his genes to carry on, but the moral act stopped them cold.
I could come up with countless more situations where morality hurts your chance to reproduce and therefore pass on those beneficial "morality genes."