Very nice work! I am not sure what method of analysis would be the most appropriate, but the sequence matrix deserves a closer look. You mention the possibility

Very nice work! I am not sure what method of analysis would be the most appropriate, but the sequence matrix deserves a closer look. You mention the possibility of one side being preferentially followed by another one, but you only investigate the simple case of the two sides being equal (preference for the diagonal). However, the correlation could be less obvious, such as one side being followed by its opposite, or by an adjacent one.