First, thanks for a truly brilliant exposition. [More along those lines, if you have not read them, are a couple of books by Lester C. Thurow on the "zero-sum society" and Spheres of Justice by Michael Walzer (all from the early 1980's).] As someone who has spent the last forty years focused on the problem of justice, I do have an idea to contribute.
As this article implied, we must distinguish between the societal processes inherent in the existence of a human community (the political process and the economy) and the outcomes for society those processes produce. Just processes will produce just outcomes--if not corrupted by unjust acts of individuals.
To get there we have to know what justice really is. My studies have taught me that it is mutual respect: most generally, taking one another into account as we live our separate lives together in this world. It does get way more rigorous and specific than that.