I get your point, I think we have a different approach to the subject.

I don't think it is a matter of superiority or being right, or closest to the truth, or finding a set of universals that apply everywhere. A subjective set of morals is still a set of moral values that can be applied by individuals to specific cases. Such sets of moral values will overlap among individuals, so and there can be agreement in specific cases (or disagreement, as the case may be). If there is sufficient overlap, such people can function together in a group and judge behaviour within that group in a fairly consistent manner, though not necessarily outside that group.

I don't think the superiority of a set of moral values needs to be somehow proven first before moral judgments can be made; no universality of codes is necessary for that. Even when subjective, judgements can be made, the only problem being, that other groups may disagree, and there not being a "universal judge" to tell who is "right". I don't think there can be, and I don't think there need be.