It's more almost, well, I hate to say this, but more a matter of definitions.
ie, what do you MEAN by the term "right"?
Just keep poking your brain about that, and keep poking your brain about what you mean by "should" and what you actually mean by terms like "morality" and I think you'll find that all those terms are pointing at the same thing.
It's not so much "there's this criteria of 'rightness' that only morality has the ability to measure" but rather an appeal to morality is what we mean when we say stuff like "'should' we do this? is it 'right'?" etc...
The situation is more, well, like this:
Humans: "Morality says that, among other things, it's more better and moral to be, well, moral. It is also moral to save lives, help people, bring joy, and a whole lot of other things"
Paperclipers: "having scanned your brains to see what you mean by these terms, we agree with your statement."
Paperclippers: "Converting all the matter in your system into paperclips is paperclipish. Further, it is better and paperclipish to be paperclipish."
Humans: "having scanned your minds to determine what you actually mean by those terms, we agree with your statement."
Humans: "However, we don't care about paperclipishness. We care about morality. Turning all the matter of our solar system (including the matter we are composed of) into paperclips is bad, so we will try to stop you."
Paperclippers: "We do not care about morality. We care about paperclipishness. Resisting the conversion to paperclips is unpaperclipish. Therefore we will try to crush your resistance."
This is very different from what we normally think of as circular arguments, which would be of the form of "A, therefore B, therefore A, QED", while the other side would be "no! not A"
Here, all sides agree about stuff. It's just that they value different things. But the fact of humans valuing the stuff isn't the justification for valuing that stuff. The justification is that it's moral. But the fact is that we happen to be moved by arguments like "it's moral", rather than the wicked paperclippers that only care about whether it's paperclipish or not.
But why should I feel obliged to act morally instead of paperclippishly? Circles seem all well and good when you're already inside of them, but being inside of them already is kind of not the point of discussing meta-ethics.
On Wei_Dai's complexity of values post, Toby Ord writes:
The kind of moral realist positions that apply Occam's razor to moral beliefs are a lot more extreme than most philosophers in the cited survey would sign up to, methinks. One such position that I used to have some degree of belief in is:
Strong Moral Realism: All (or perhaps just almost all) beings, human, alien or AI, when given sufficient computing power and the ability to learn science and get an accurate map-territory morphism, will agree on what physical state the universe ought to be transformed into, and therefore they will assist you in transforming it into this state.
But most modern philosophers who call themselves "realists" don't mean anything nearly this strong. They mean that that there are moral "facts", for varying definitions of "fact" that typically fade away into meaninglessness on closer examination, and actually make the same empirical predictions as antirealism.
Suppose you take up Eliezer's "realist" position. Arrangements of spacetime, matter and energy can be "good" in the sense that Eliezer has a "long-list" style definition of goodness up his sleeve, one that decides even contested object-level moral questions like whether abortion should be allowed or not, and then tests any arrangement of spacetime, matter and energy and notes to what extent it fits the criteria in Eliezer's long list, and then decrees goodness or not (possibly with a scalar rather than binary value).
This kind of "moral realism" behaves, to all extents and purposes, like antirealism.
I might compare the situation to Eliezer's blegg post: it may be that moral philosophers have a mental category for "fact" that seems to be allowed to have a value even once all of the empirically grounded surrounding concepts have been fixed. These might be concepts such as "would aliens also think this thing?", "Can it be discovered by an independent agent who hasn't communicated with you?", "Do we apply Occam's razor?", etc.
Moral beliefs might work better when they have a Grand Badge Of Authority attached to them. Once all the empirically falsifiable candidates for the Grand Badge Of Authority have been falsified, the only one left is the ungrounded category marker itself, and some people like to stick this on their object level morals and call themselves "realists".
Personally, I prefer to call a spade a spade, but I don't want to get into an argument about the value of an ungrounded category marker. Suffice it to say that for any practical matter, the only parts of the map we should argue about are parts that map-onto a part of the territory.