First, thanks for another intelligent, insightful article.
As suggested in this article, one aspect of modernity was replacing theology with ideology for governing governance. One ideology, Liberalism, sought to get at what justice 'really is'. Liberal philosophers didn't get there, but it is possible to see what justice really is from where they did get: equality and liberty as the 'twin pillars of justice' for a just society. That did represent progress in the biggest way possible.
The problem with using ideology to arrive at the correct understanding of justice is that ideologies are based on beliefs as surely as any religion is. Beliefs divide people and all people's beliefs are, from the point of view of any other person, completely arbitrary. They are purely subjective. They lead to irresolvable “contests of power” (from Michel Foucault).
The ethic of justice must follow from observation within material existence. That is not arbitrarily 'privileging' the scientific point of view. Rather, material existence provides human beings with a verifiable commonality of experience/knowledge that no belief ever could.
As it happens, I have developed such an approach to justice. It would take us "Beyond Liberalism" (here in Medium but not behind the paywall).