It's a philosophical term, not a LessWrong one, and I've usually seen it defined as something like "examining moral judgments about a particular issue by looking for their coherence with our beliefs about similar cases and our beliefs about a broader range of moral and factual issues.".

I'm not sure PhilGoetz is using it that way.

The virtues expressed in the Iliad are pretty close to a reflective equilibrium

seems hopelessly far from the standard understanding of reflective equilibrium, which requires "subjecting the views we encounter to extensive criticism from alternative moral perspectives". No one does that in the Iliad. But I am still confused about PhilGoetz's point, so I may be missing something.