I always thought the term 'libertarian socialist' was kind of funny, since libertarianism and socialism are more or less on the opposite ends of the political spectrum. An oxymoron, if you will.
And secondly, like many people have probably said, I find the theory more or less naive, and impossible without killing off over 90% of the global population evenly across the world and destroying every single remnant and parcel of knowledge of post-Neolithic technology, and only then to probably have the system of hierarchical society reappear eventually. For you see, while somewhat ecclesiastical societies have been documented, they all have been very small groups of hunter-gatherers or limited subsistence agriculturalists. Small size is necessary because while a small group of people can probably manage themselves without a clear hierarchy, a significantly larger group of people introduces more chaotic elements, what with more people expressing more viewpoints and being unable to negotiate about them as easily as with the small group. Such a group would need a form of organization to perform, one that involves specialization and hierarchy. And if you were to say, "Well then, everybody can be in small groups, why does the population need to be small?" well, a lot of people means a lot of competition for resources that would not be scarce if there were less people. In competition for these resources, the groups would probably coalesce and organize into organized hierarchical societies in a bid for more efficient gathering, raising, and production of resources, and would dominate the other groups unless they have organized like said group, or make make an alliance with other anarchistic groups to bring down the organized group, which would likely fail as a) at that point there are probably many such supergroups, b) the supergroup could very well lure the offending groups into joining to reap in the extra resources, c) the supergroup, with more resources than the other groups could easily bribe some of the offending groups off with resources, and d)the disorganization of the alliance would work in the organized supergroups favor, and a martial organization of the alliance would probably take over the alliance and make it into a supergroup. So the population has to be thin enough so there is no significant conflict over resources.
As for technology, well, if you want this kind of society, you can forget about anything above lower Neolithic. As I said, the anarchist society cannot function above small groups, but significant technology requires large groups. A single person can make a stone axe from scratch, for example, but a machine gun requires the effort of a ton of people with different types of expertize to mine and refine the materials, to shape them, put it together, and maintain it. All of this requires the sort of organization you can't have. Also, the only thing sustaining our current population is technology, so remove that and plenty of people will die. And even with technology halted, the technology left around will create a valuable scarce resource made only scarcer. One can expect competition for technology, reenacting the above scenario. And even after improbably destroying all remnants of technology before they are exploited, you have to make sure all knowledge of making technology is gone, lest anyone recruit an empire on the promise of returned technology.
Also your vision of Native Americans is a bit heavily romanticized.