I’ll admit that the naturalization of moral value is a more difficult philosophical problem than my reply let on - I simplified. But the essence of my argument remains the same.
I’ll first say that I don’t disagree with the substance of your counterarguments.
Moral sentiments are just physiological states. They evolved to serve the inclusive evolutionary fitness of our genes. Change the genes (hypothetically), environment and/or social situation of a human organism, and the morality that it adheres to may change. But I can say roughly the same of physics. The ability to do physics evolved only because the requisite cognitive capacities happened to serve the fitness of our genes in the ancestral environment.
Within any sane epistemology, the contingency of a view with respect to environment or biology is irrelevant to its objectivity. Likewise with the (pseudo-)problem of there being multiple viable moralities. Here I’ll analogize to economics: when an economic problem arises, economists may have a difference of opinion. They will propose solutions to the problem on the basis of their opinions. Is it wrong to say that multiple economists can have different yet objectively correct solutions to the problem - correct by reference to the axioms of economics?
Morality is emergent. But so too is psychology, economics, biology, chemistry, etc. At bottom, everything is just physics. Morality is emergent from physics in the sense that the qualia (i.e experience) of suffering and wellbeing (which I take as the metric of value, the axioms on which morality rests) are an expression of the laws of physics.
All objective schools of thought (emergent or not) rest on axioms that cannot be proven by reference to the school of thought itself. Of physics, we can say that it is our best effort to make sense of matter and energy. Of morality, for it to be sound, I think it must be ‘our best effort to understand good and bad.’ As soon as you grant the axiom that bad refers to pointless suffering of the worst kind imaginable, morality as a whole is rendered objective.
I argue this as someone generally sympathetic to a Nietzschean [or biofoundationalist] perspective - morality is an expression of a human’s physiological states. A person’s morality is diagnostic of their character and worth. Although I think consequentialism accurately describes moral truth, I don’t usually think like a consequentialist - that would be an indictment of character.