In feel like you make it complicated to arrive at your conclusion here. Communism, as described by Marx and Engels and to some degree Lenin, is something very specific that covers most aspects of the society. Political, social and economic. Marx himself wrote books upon books on the economy of a socialist, communist system.
It is not an abstract "I don't like capitalism so let's try something different" approach. And yes, many have tried to adapt it, as you mentioned which is why those different approaches carry a different name 'anarchist communism' in your example. Because they are different enough from flat out communism.