That's no more true for social justice than for any other view or principle held by many. There is in fact a large established body of work exploring what social justice means and exploring the concept in excruciating detail, from the Englightenment through Rawls, Nozick, and others. Yes, everyone brings their own personal interpretation, but so does every liberal, white nationalist, feminist conservative, Nazi, libertarian, etc. Singling out social-justice theory, when it's among the most developed of these ideas, is absurd.
> So the challenge is to either disagree, and identify fixed moral positions/values that support "social justice"; or to agree that social justice is moral relativism
As I said, I often do that, but not within an opponent's frame according to their priorities and subject to their judgment of which answers are sufficient.
> third parties who can't tell the difference may find it convincing
And if it's called out clearly enough, those same third parties might find it singularly unconvincing and be put off by the attempt to instigate a false debate.