"communist / marxist regime per se - at least not that I know of."

Based on what you said there, I don't think you have an understanding of what communism or marxism are. Marxism is a set of economic theories mainly based on understanding capitalism, and not a system itself. (It is a system in the negative sense, as it seeks to abolish what exists today.)

Communism is worker control of the means of production. I have a feeling most places you are thinking of, like Soviet Russia, were based on the ideals of what I would call "state socialism". The idea that using capitalist political structures will allow communists to keep power over the capitalists (sounds like a real smart idea, lol).