Here are the results of another attempt. This time I used Nikon's Camera Control software to do the focus adjustments. It has buttons that let you adjust the focus distance in small increments. this image was the result of a stack of (20!) images. Even still, I missed sharp focus on the closest and furthest parts of the image.
I also found that Photoshop's auto-merge feature doesn't always select the sharpest layer perfectly. I went in and adjusted the layer masks and was able to "paint in" sharper focus on some additional areas. Clearly this takes a lot of fine-tuning and adjustment.