If you have already worked out an EI which you are satisfied with, I suggest the problem is either as Ralph suggests, that Zone III is actually darker than you are visualizing or that you are measuring the real life scenes incorrectly. For example, Canadian winters are full of snow and if I meter for shadows while taking a winter shot, all of my highlights are blocked up because the snow is so bright. I could reduce the development (N-1, N-2), try a compensating developer (stand development or a water bath) or I can accept the fact that the scene exceeds what my film/paper is capable of reproducing and make a decision as to what the most important zone in the scene is and use that as my baseline. Often (in winter snow scenes), I use the snow as my zone VIII basis and let the shadows fall where they may. I do this as snow without texture/detail looks worse than shadows with insufficient detail for a winter scene, in my opinion. For summer scenes, I can't live without the shadows.
Thus, I am not trying to criticize your method but if you slavishly adhere to zone III being the only important zone (as many "zoners" are apt to do), I think you miss the point of the system. You need to decide what the final print is supposed to look like, what tones are going to be important in that print and then meter for what is important. While "expose for shadows, develop for highlights" is a good start (and end point), it is not a final methodology in itself. No one here is advocating having too rigorous a mindset that photographers too often fall into. If you read St. Adams books and printing methods, he often metered for something else besides zone III because that was what he wanted the final print to emphasize.
That said, zone III is much darker than most people realize.