I haven't been able to find a way to add a shared row header across multiple subplots, as in the figure below. I don't want to use the xlabel of any plot, both because I need the label and because they don't align in the center of the row. I'd appreciate any suggestions.

Is this six different subplots? Maybe see Text in matplotlib helps you. http://matplotlib.org/users/text_intro.html Consider this is not title but a text at an arbitrary place.