First, thanks for such a cogent, informative essay.
If I may, I would say that rationalism, as a vehicle for arriving at an ethic for governing human relations, has suffered most of all from a lack of rationality. All 'rationalist' attempts at discerning any such 'ought' have contained non-rational, immaterial truths, including Hegel's "’World Spirit’," Kant's "noumenal" realm, and "equality" and "Natural Rights" in Liberalism.
There is, however, "an immutable, ahistorical, and universal human nature" (from the essay) that all humans have always shared, and presumably always will: as noted, in fact, in the essay, we are, as Locke put it, "separate and independent" beings yet also social beings. His and other "social contract" theories have been intended to reconcile those two aspects of our nature--unsuccessfully.
Here is another eternal truth about human beings: we have no choice but to effect choices (which I got from Warren J. Samuels). That makes choosing integral to being human. That is a starting point for a truly universal ethic: to recognize one another as fellow humans is to respect one another's capacity to choose--beginning with choosing whether/how/to what extent to be involved whenever any choice is being effected.
A society governed by that ethic would have the maximum liberty that coexisting people can share simultaneously--as a product of justice, not its source, or foundation, or predicate, etc. 'Equality' would be rendered an unnecessary complication: all that matters for justice is that the beings involved are humans. A Liberal society that came to be governed by the ethic would not have to make any changes to its institutional structure, but its functioning--its effects on people--would be transformed, especially in the economy.
if curious: "A New Liberalism" (here in Medium, but not--for the benefit any 'guest readers'--behind the paywall)