Of course the criticism of a religious origin of the good is on target, but I think that the alternative that you have not explored here is the idea that the good is a matter of the achievement of goals and how to do so. So for example, if I have a goal to go to New York then certain things will promote the achievement of that goal while others will inhibit it. Thus we can say that this is a good spoon or a good sentence because it fulfills the goals appropriate to a spoon or a sentence. We can also ask the same question regarding a person.
Of course, all of these kinds of goals and means don't exist in a vacuum. Certain ends precede or promote others (for example, getting some money will tend to help you get to New York among a whole lot of other things) and certain means tend to reinforce others as well. There are plenty of general choices that are generally beneficial to the achievement of ends and some that are generally antagonistic to them as well such as honesty, productivity, education, having friends, and so on. These more general alternatives correspond pretty well to the general moral virtues don't you think?

Weird that you have Alex Millar from Birmingham University where he hasn't been for at least 5 years, maybe more.
How long ago was this show recorded?

I think that the "moral good" is a basic human good and that it primarily supports and interacts with the good of "life". In addition to the moral good and life, I regard purposefulness, aesthetic experience, knowledge, friendship, and play as the other basic human goods. I believe these basic human goods are incommensurable, irreducibly simple, and comprehensive -in that one can build with them a comprehensive theory of human value. This set of basic human goods as analytical concepts can also be used to deconstruct down to the level of value any institution or idea.

I appreciate Alex Miller's analysis, but I think that if we really interrogate and refine his standard of "promoting the well being of sentient beings," we get utilitarianism, which Rawls pretty convincingly refuted.

There is no absolute morality, because the ideas of 'good' and 'bad' assume some sort of external scale to which all of our humanly actions must be weighed against. A good action to one may not neccessarily be a good action for another(ex, by killing the enemy soldier, I am doing a good deed for myself and my country, but not to the opposing forces.)So, by saying that something is 'good' and something is 'bad', you are almost laying out an objective list of criteria for one to follow in order to be 'good', which would necessitate some sort of supreme, omnipotent being.
Morality comes from humans will to power, or will to freedom. In order for one to act in a 'good' sense, it must be in a way as to promote the freedom of others. Now, this is not in an absolute sense, where there are objective criteria for how to promote this freedom, but more in such a way that it lays out the basis for a future, undetermined system of values in such a being. The only way to act in the ethical is to promote the freedom of others, because it allows for personal freedom. If one does not promote others freedom, and has them acting according to their agenda, then that person is not truly free. Their lives are being controlled or determined by their own master-slave relationship to The Other, and their lack of freedom. It is only when the individual promotes The Other to act freely that one can live in an ethical way, for this is the only way that the individual can live freely, and our personal freedom is the only body that governs absolutely over our behaviour.

Alex Miller,
Concerning "Where does Morality Come From?" I understand the problem with what you call a truism. The focal point seems that it can be more accurately termed circular reasoning and this would, or at least should, make the reason repugnent to a non-theist. As with you I think there is a better way to go at this and it is from nature. As one might say it is "the nature of the beast" that determines moral right or wrongness. It seems to me that any act that violates the good of the being under moral scrutiny is a bad act. Conversely, any act that upholds the good of a being must be morally good. Each being has a nature and we find from this nature comes certain requirements to maintain it's wholenss and integrity. For instance a flower requires food, water and sunlight for the maintenance of it's health. There are other things required depending upon what aspect of the being's nature we are considering and each being has it's own necessary goods, so to speak. In context of the example you posed, Granny Smith's nature as a human person requires she be treated in this way and not some other. In comparison to a flower she has similar requirements as well as others that are particular to her higher nature as human. Whereas she might need to "feel less lonely" a flower would not have any such need. Either way moral truth is determined by the being under consideration.
So I agree with you the question of morality "is independent of whether I *think* that it promotes her well being (and probably also independent of whether *she* thinks that it promotes her well being)." It is first and foremost an objective criteria based on Granny's nature independent of what anyone thinks. And as you say there is "no God involved" here so it should be acceptable to, say, an atheist. At least on the surface the question of deity does not have to come up. The only reason an atheist might not agree with this reasoning is that they don't see reality as clearly as they should. They might see something contrary to the flower or Granny's nature as being good when we know it is not. Nevertheless, this argument for moral authority can be called the natural law (not to be confused with science's laws of nature) or in other words the argument from conscience. So it all depends on how clear one's perception and intuitive understanding into the nature of a being is as well as their clarity of conscience.
Now what is good about this position is that it leads right up to God without having to invoke Him. If one can get a clear minded atheist to agree with it the next step could be taken of introducing the more substantial basis for this argument. That of cause and effect: we have a nature, we have an intellect and a conscience with which to distinquish between right and wrong precisely because these are effects. We do not cause ourselves nor the powers of body and soul we utilize. As effects they are dependent upon a Cause that has these effects within itself. We can get into the finiteness of our powers of intellect and conscience and the infinite Source they mirror, but they in themselves point directly to the absolute moral Authority from which we know all authority comes. Thus morality has it's basis first in God and secondarily in our nature which reflects God's nature.