First of all, thank you for such an erudite article on such a deeply important topic. I hope a lengthy Response will be taken kindly.
I really like the idea of anarchy as the absence, not of order, but of arbitrary power in human relations — some people imposing their wills on others, as Locke had it. That in turn establishes a link between democracy and anarchy. Democracy is self-government in the sense of 'the people' as the ultimate locus of sovereignty as well as people as individuals taking it upon themselves to govern their own actions.
Still, are "freedom and autonomy fundamental properties of human nature?" Materially, what we can know for certain is that humans are — and have always been — social beings: living together in groups we have come to call 'societies'. Co-existing in societies necessarily limits freedom and renders autonomy null and void (compared to living as isolated individuals would be).
For any society even to exist choices must be effected for the community as a whole. That is unavoidable. The process of effecting choices for the community as a whole is what we commonly refer to as the political process.
So the most fundamental issue related to human relations is to carry out the necessary function for the existence of society — effecting choices for the community as a whole — without the presence of arbitrary power. As this article suggested, at the bottom of that issue is a problem of reflexivity: how can a just (non-arbitrary) political process be established without involving arbitrary power in any way? In short, what is a just political process?
To know that we must know what justice is. There we encounter another reflexivity problem: to arrive at an ethic of justice — a rule for governing the conduct of all human beings — that does not involve any person or group arbitrarily imposing their beliefs (or opinions, feelings, etc.) on any others.
To get there we have to go to our shared material existence as human beings. Only an ethic following from that shared existence can have the inherent universality justice requires, such that no person can (legitimately) deny the applicability of that ethic to all human beings, including oneself. Only in that way can an ethic of justice to govern human relations be utterly non-arbitrary.
"Real Justice (summarized for a '5 min read')" (here in Medium)