First of all, thank you for such an edifying essay.
I thought you might find interesting an account of justice that is 'falsifiable' because in it the ethic of justice follows immediately from observation within material existence. ‘Real justice', as I call it, divorces justice from morality.
Real justice contains no beliefs. Beliefs (radically subjective truths that are divorced from material existence) are non-falsifiable, but they have been the basis of morality for all of human history. Justice has been deemed to be some part of morality.
Real justice represents a "paradigm shift" (going from Popper to Kuhn). One might say it is similar to going from Newtonian to Einsteinian physics, but real justice takes justice from the unfalsifiability of beliefs to sufficiently verified knowledge within material existence.