I'm not a proponent of anything Authoritarian, but communism on a small scale does fascinate me.
This is an important distinction. Humans evolved in tribes, and many of our instinctual responses to how we think we should work together are optimized for such a setting. But these things just can't scale upwards. There are many things that work well at a community level that fall apart with larger groups. So when we see a problem in the world and feel our heart-strings tugged, we should be suspicious that our emotional response is something that can really make sense in the big picture.
I do agree that such things might be able to work at small scales. But I suspect that the threshold is well below the size that you're citing here.
Markets work because they are irrational, and move with people as situations change - like a subconscious reflex - planned economies require conscious effort to reapportion their efforts in the face of change.
The solution to socialism is collectives - lots of little ones from 50-500 people, which then interact with each other using market settlement and price adjustment mechanisms.