We can have objective reasoning to support our own notion of justice, and that can be widely agreed upon - but it won't be universally agreed upon.
I make that judgment frequently.
Justice is real to me, and it turns out that some of the basics of my definition of justice coincide with that of others. For example, my definition says rape is unjust. That's pretty widely agreed upon, although it's obviously not universal. If enough of us have the same definition for a particular action, then a cultural norm arises. Cultural norms aren't always right, though. Slavery was a cultural norm for centuries. Culture changed, and its definition of justice changed along with it.
So you are appealing to your sense of justice as purely a learned and human convention/invention.
What I would ask you to consider is that one can take for granted that things learned must be human convention. Example, the multiplication table, it is certain we are taught this, but whether we are taught it or not does not make the table any truer or not. So in arithmetic we may get false sums, but we correct for it and progress. It is this progress that allow the multiplication table to be a standard by which we can compare our progress.
So to I admit we learn decent behavior from our parents, schools, books etc... This must not mean that it can only be a human convention. If our morals can be said to improve over time or from nation to nation, we must have some standard by which to make this comparison, if not there is no difference in savage morals or decent morals.
What we find in your cultural example is that the moral law existed just as the multiplication table existed, we just were missing the mark and still do plenty of times, but we must ask which class the moral progression really belongs too, real truth or human convention.
So, have I not given a reason to wonder if indeed moral law or law of human decent may be a real thing?