Very interesting post. Great quality !
However, I do not think that the essence of anarchism is directly related to who owns the mean of productions. As a matter of fact, the question of the mean of productions truly became central in the political philosophy with the quick development of the capitalistic society. Numerous anarchist societies were not concerned by who owns the mean of productions. One example is hunter-gatherer societies. They only use their body to hunt, and the forest belongs to everyone. So for some of them it would make no sense to argue who should own the mean of productions.*

To be clear, I am not saying that your argument is invalid. It is valid. My point is, you made a very important choice by picking a specific lens with which you consider this situation. This lens being : "the central question is : who own the mean of productions ?" To me it's not. I would say that anarchism is first and foremost answering the question of : "Who should take decisions for society ?" by "society itself". I feel like it is important, because who owns the mean of production is the direct consequence rather than the cause of the answer to this question.

To me - and I may be wrong - anarchism is by essence a way to bring democracy, which is a bigger picture than just the control of the mean of productions. You're absolutely right to focus on it because authors of this period do speak a lot about it. In my opinion, it's because it was the main issue of their time rather than because it was the essence of their philosophy. In the future, automatisation and the sharing economy (among other things) will replace this issue by others. However, it does not disqualify the essence of their philosophy.

Sorry my message is very long ahah, I'll write more on this later. To sum it up, all socialism share the same goal, which is more or less : "make a better society by improving the life of the majority and diminushing inequality". The timeless debate being how to achieve this goal ? For anarchist, we just organize ourself, but it did not work because everytime they were crushed by the government -> enter communism, that solve this issue by saying we have to seize the power. It fails mainly because "absolute power bring absolute corruption", an argument that was already present in anarchist philosophy -> after that, only the weakest of the three brothers, social-democracy, stays afloat mainly because it is not as threatening for the elite. The question of who owns the mean of production was only one episode, at a specific period, of this battle. With that being said, your post was very good !

*I am aware of a few book that deal with this issue. One of them that I would recommend is "Fragments of an anarchist anthropology" by LSE professor David Graeber.