"Communism is less about an end goal, and more about a continuous process"
This is how I think about my own anarchism.
I don't disagree with you that class distinctions would naturally arise from the systems of production and distribution, but I don't see that as a problem really. There are some features of human society that feel analogous to gravity, in that they exist as functionally immutable forces that we must learn to navigate around and through. Even if we somehow achieved what we would consider to be a utopia, it's realistically not going to stay that way — there would inevitably be some event or new development that would disrupt the balance of things. Such change isn't necessarily bad, especially if we respond to it properly. It is inevitable though, which is why I find it useful to think of it as a process. I can't remember who I heard this from, but a phrase I like is "my goal isn't to make anarchism, but to make more anarchists"
I don't consider myself a communist, but I like your comment because it highlights how much we have in common. A communist society wouldn't necessarily be non-anarchist, and vice versa.
For now though, I find myself happy to shelve most ideological disputes with communists, because we're so far away from either an anarchist or communist society that it seems more productive to use our common ground to strive towards a world that both of us would agree is better.