Cognitivist normative and metaethical relativism

Cognitivist normative moral relativism is the thesis that for all x and A:

1. x morally ought to A if and only if x believes that she[note 1] morally ought to A.

(Notice that one then has to drop "ought implies can".) Cognitivist normative moral relativism is a thesis at the normative level that tells us what, in fact, is obligatory.
Cognitivist metaethical moral relativism wants to add to (1) a parallel account of what it is to have a moral ought. I want to spend this post thinking about whether this can be done. The simplest attempt is:

2. What it is for it to be the case that x morally ought to A is for x to believe that she morally ought to A.

But this is viciously circular, since "morally ought" appears on both sides of the definition.
But perhaps there is some way of redescribing the belief without mentioning its content. Maybe, for instance, there is some "pragmatic" account of what it is to believe that one morally ought to A in terms of patterns of emotion and behavior. But that threatens to become a non-cognitive account, and it is cognitivist moral relativism that we're looking at. (Maybe, though, one has a pragmatic account of all belief and cognition? If so, then maybe one can run this line.)
Or maybe there is some other "ought" that one can put in the definiens in (2). Perhaps, what it is for it to be the case that x morally ought to A is for x to believe that she simply ought to A, or for x to believe that she all things considered ought to A. Let's take the second option for definiteness—any similar proposal will have the same problem.
Then, the belief that one morally ought to A and the belief that one all things considered ought to A either are or are not the same belief. If they are the same belief, our modification of (2) remains circular, since "all things considered" is just a synonym for "morally". And if they are not the same belief, then we get an account that surely conflicts with (1). For if they are not the same belief, then someone could believe that she morally ought to A without believing that she ought all things considered to A. By the analogue of (2), it is not the case that she morally ought to A, and by the analogue of (1), it is the case that she morally ought to A.
So, it is difficult to come up with a cognitivist relativistic metaethical theory that neatly matches (1). One might give up on cognitivism, but then one needs to modify (1), since (1) commits one to beliefs about what one morally ought. The other move is to accept (1) but couple it with a non-relativistic metaethics. For instance, it is prima facie coherent to conjoin (1) with:

3. What it is for x to morally ought to A is for God to command x to A.

If one wants one's normative ethics to hold necessarily, one should then say that necessarily God commands everybody who is capable of moral beliefs to do what they believe they ought to do and that he commands nothing that goes beyond that. Such a metaethically absolutist normative relativism is fairly coherent, but also not plausible. Why think that God commands this and nothing beyond this? Similarly with other views, like natural law or virtue ethics, that one can plug in metaethically. The resulting theory may be coherent, but it does not appear plausible.
But there is one version of the theory that is kind of interesting. Suppose that

4. Necessarily, if God made persons other than himself, then out of a concern for their moral life he made them in such a way that they believe that they are morally omniscient, where x is morally omniscient provided that (x believes that she ought to A) if and only if x ought to A, and x knows that she ought to A if and only if x believes that she ought to A.

One could couple (4) with any metaethics compatible with theism, and then one gets (1) as a consequence. Of course, on its face, (4) appears pretty implausible when conjoined with a non-relativistic metaethics. There seems to be too much moral disagreement. To make (4) plausible on non-relativistic metaethics, one might have to combine (4) with a view on which people have all sorts of moral beliefs that they apparently don't know about. But notice that at this point we've departed quite far from the spirit of relativism.