My studies have taught me that the problem with trying to use equality to achieve justice is that equality is not an ethic. It is not a rule to govern interactions among human beings.
Equality does however yield an ethic: mutual respect, i.e., taking one another into account as we live our separate lives together in this world. Mutual respect is the ethic of justice, the ethic that must govern interactions among human beings all the time, everywhere. A society governed by mutual respect would have the maximum liberty that coexisting human begins can share simultaneously.