It is easy to read a sundial with an accuracy a bit better than the solar diameter, even if the shadow is from a simple edge. The worthy goal of a shadow sharpener is to significantly improve on that accuracy. Since we still want to make the reading with a human eye, the "best" system will be determined to a large extent by psychophysics. Human vision is so complex that it is not obvious just what we are looking for, so the final judge will be experiments.
Nevertheless, I have a feeling that it may not be possible to improve on a simple pinhole. The image produced by any of the systems discussed (a simple pinhole, an annular pinhole, or a classical shadow sharpener which is a pinhole "downstream" of a conventional gnomon) will be sharper if the holes are smaller, at the expense of brightness. It may be hard to find with arbitrary accuracy the center of the image produced by a simple pinhole even if it is perfectly sharp, but one should be able to locate the edge of the image as accurately as desired. I would thus suggest to the experimentalists that they always compare the clever designs with simple pinholes, where the pinhole diameter should be varied to find the optimum, and where both forms of reading, from the center of the image and from an edge of the image, are compared. A simple pinhole may also be less sensitive to variations in the distance to the scale and gross variations in the position of the sun during the course of the day. On the other hand, reading from the edge of an image may be less intuitive for the casual user of a dial. Cheers, Art Carlson
