A bigger problem that "tighter" is, I think, the point of departure for a candidate for 'ethic of justice'. "Fairness" is based on a nonmaterial point of departure: 'equality'. Mutual respect can also be arrived at from an belief in equality (and other nonmaterial premises), but it also follows from a fact of material existence. Esoteric debates about 'free will' and 'agency' cannot trump that fact of material existence.
In real justice the concern is actions involving fellow humans in effecting choices. We know from experience of material life that everything included in that sentence exists. None of that other stuff can be materially known to exist--or not exist.
Anyone can rationally deny any point of departure for the ethic of justice that is non-material. No one can rationally deny that human beings have no choice but to effect choices, which makes choosing integral to being human.
That is where arbitrariness enters the picture. In the end either accepting or denying any nonmaterial premise is an act of arbitrariness (at least form the point of view of any other person). It is also an act of arbitrariness to deny realities of material existence. It is not an act of arbitrariness to accept realities of material existence. The more commonplace those realities are, the more blatantly arbitrary denying them is. There is no more commonplace reality of material existence than the observation that human beings have no choice but to effect choices.
As for 'tightness' itself, it's hard to get tighter than an absolutely universal absolute prohibition on killing, harming, coercing, stealing, and manipulating (in effecting any choice). Meanwhile, mutual respect (not 'equality') already governs the democratic political process and I have spent my adult life understanding how it (as opposed to 'equality') can be applied to the economy, for (adult) citizens it absolutely, positively eliminating unemployment and poverty (and possibly taxation) without taking anything from anyone. What can be 'fairer' than that?
Finally, mutual respect makes sense of the place of liberty in a just society. It is the product of justice, not its source, or foundation, or predicate, or "lexically prior" good, etc.
In any form of contractualism either the outcomes must be 'lexically prior to' the process or the outcomes of the process must be open-ended to the point that, say, feudalism--or Hobbes's version of an Ubermensch--is a possibility.
In the end, I just can't see how can mutual respect be "fuzzier" than "fairness" is.