First, thanks for an informative article. I had read Part 2 previously. The tie-in with Deleuze' s thought was especially interesting.
The problem with Rawls's approach to justice is that his account of justice lacks what is most necessary: universality. It is limited to, at the most, people who accept the Liberal meta-ideology, with equality and liberty as the 'twin pillars of justice' for society He is straightforward about that, but it is a fatal weakness for "a theory of justice" nonetheless.
Rawls acknowledges that transcendent truths of all kinds, including truths regarding morality/justice, are potentially universal, but in practical effect self-limiting to those who accept any such truth as valid. Anyone can reject the validity of any profession of such truth. Accepting/rejecting such truths is a deeply personal mater.
That does include, though, the 'truth' that equality and liberty are the twin pillars of justice for society. We are seeing that even among people who accept that truth, differences in assessing the relative importance of each can be destructively divisive.
Justice requires universality because universality is the antidote to arbitrariness--which Locke, the originator of Liberalism, equated with injustice as his starting point in his account of justice. With transcendence unavailable for universality, that leaves observation within material existence as the source of a universal ethic of justice. To fulfill that role it must be a patently true observation that anyone can verify for oneself.
I have developed such an account of justice. The ethic of justice follows from the observation that human beings have no choice but to effect choices (which I got from Warren J. Samuels). That makes choosing integral to being human, so recognizing one another as fellow human beings entails respecting each other's capacity to choose--beginning with choosing whether/how/to what extent to be involved whenever any choice is being effected.
The ethic of justice is thus 'mutual respect in effecting choices'. Recognizing that as the ethic of justice would take us "Beyond Liberalism" (here in Medium, but not behind the paywall).