When you said that "moral" is "that which one should do" you simply failed to delve into a more fundamental level that would describe what the terms 'moral' and 'should' both refer to.

One can only fail to do what one is trying to do. If what one is trying to do is refute a putative definition of "morality" one doesn't need a full reduction. AFIACT, that was in fact the context -- someone was saying that Clippy could validly define "morality" as making paperpclips.

My own view, for example, is that our moral sense and our perception of what one 'should' do are an attempted calculation of what our preferences would be about people's behaviour if we had no personal stakes on the matter -- imagining ourselves unbiased and uninvolved.

I like that idea too -- although It isn't new. Also, it is a theory, not a definition.

Assuming the above definition is true (in the sense that it accurately describes what's going on in our brains when we feel things like moral approval or moral disapproval about a behaviour), it's not circular at all.

Does physics shave to describe what we think the behaviour of objects is, or can we improve on that?

My own view, for example, is that our moral sense and our perception of what one 'should' do are an attempted calculation of what our preferences would be about people's behaviour if we had no personal stakes on the matter -- imagining ourselves unbiased and uninvolved.

That is not a definition of morality, that is a theory of morality. (It's one of the better theories of morality I've seen, but not a definition). To see that that is not a definition consider that it appears to be a non-trivial statement in the way that a simple statement of definition shouldn't be.