I'm a moral cognitivist but not a moral realist. I have laid out what it means for my moral beliefs to be true

Even among philosophers, "moral realism" is a term wont to confuse. I'd be wary about relying on it to chunk your philosophy. For instance, the simplest and least problematic definition of 'moral realism' is probably the doctrine...

minimal moral realism: cognitivism (moral assertions like 'murder is bad' have truth-conditions, express real beliefs, predicate properties of objects, etc.) + success theory (some moral assertions are true; i.e., rejection of error theory).

This seems to be the definition endorsed on SEP's Moral Realism article. But it can't be what you have in mind, since you accept cognitivism and reject error theory. So perhaps you mean to reject a slightly stronger claim (to coin a term):

factual moral realism: MMR + moral assertions are not true or false purely by stipulation (or 'by definition'); rather, their truth-conditions at least partly involve empirical, worldly contingencies.

But here, again, it's hard to find room to reject moral realism. Perhaps some moral statements, like 'suffering is bad,' are true only by stipulation; but if 'punching people in the face causes suffering' is not also true by stipulation, then the conclusion 'punching people in the face is bad' will not be purely stipulative. Similarly, 'The Earth's equatorial circumference is ~40,075.017 km' is not true just by definition, even though we need somewhat arbitrary definitions and measurement standards to assert it. And rejecting the next doesn't sound right either:

correspondence moral realism: FMR + moral assertions are not true or false purely because of subjects' beliefs about the moral truth. For example, the truth-condition for 'eating babies is bad' are not 'Eliezer Yudkowsky thinks eating babies is bad', nor even 'everyone thinks eating babies is bad'. Our opinions do play a role in what's right and wrong, but they don't do all the work.

So perhaps one of the following is closer to what you mean to deny:

moral transexperientialism: Moral facts are nontrivially sensitive to differences wholly independent of, and having no possible impact on, conscious experience. The goodness and badness of outcomes is not purely a matter of (i.e., is not fully fixed by) their consequences for sentients. This seems kin to Mark Johnston's criterion of 'response-dependence'. Something in this vicinity seems to be an important aspect of at least straw moral realism, but it's not playing a role here.

moral unconditionalism: There is a nontrivial sense in which a single specific foundation for (e.g., axiomatization of) the moral truths is the right one -- 'objectively', and not just according to itself or any persons or arbitrarily selected authority -- and all or most of the alternatives aren't the right one. (We might compare this to the view that there is only one right set of mathematical truths, and this rightness is not trivial or circular. Opposing views include mathematical conventionalism and 'if-thenism'.)

moral non-naturalism: Moral (or, more broadly, normative) facts are objective and worldly in an even stronger sense, and are special, sui generis, metaphysically distinct from the prosaic world described by physics.

Perhaps we should further divide this view into 'moral platonism', which reduces morality to logic/math but then treats logic/math as a transcendent, eternal Realm of Thingies and Stuff; v. 'moral supernaturalism', which identifies morality more with souls and ghosts and magic and gods than with logical thingies. If this distinction isn't clear yet, perhaps we could stipulate that platonic thingies are acausal, whereas spooky supernatural moral thingies can play a role in the causal order. I think this moral supernaturalism, in the end, is what you chiefly have in mind when you criticize 'moral realism', since the idea that there are magical, irreducible Moral-in-Themselves Entities that can exert causal influences on us in their own right seems to be a prerequisite for the doctrine that any possible agent would be compelled (presumably by these special, magically moral objects or properties) to instantiate certain moral intuitions. Christianity and karma are good examples of moral supernaturalisms, since they treat certain moral or quasi-moral rules and properties as though they were irreducible physical laws or invisible sorcerors.

At the same time, it's not clear that davidpearce was endorsing anything in the vicinity of moral supernaturalism. (Though I suppose a vestigial form of this assumption might still then be playing a role in the background. It's a good thing it's nearly epistemic spring cleaning time.) His view seems somewhere in the vicinity of unconditionalism -- if he thinks anyone who disregards the interests of cows is being unconditionally epistemically irrational, and not just 'epistemically irrational given that all humans naturally care about suffering in an agent-neutral way'. The onus is then on him and pragmatist to explain on what non-normative basis we could ever be justified in accepting a normative standard.