I finally figured out the major issue I was having with my tablet weaving, after consultation with everyone I could think of who might have insight into the problem.
It turns out that I had been thinking of the labels on the paper cards as being meaningful in themselves rather than as referring to thread positions. So once I made sure my S cards and Z cards were facing the right directions, I rotated the Z cards so the blue thread positions mirrored those on the S cards (as specified in the pattern). That worked perfectly, and now I have something approximating the desired pattern.
The pattern is supposed to alternate knotwork portions and a different diamond-y design. As you can see from the above pictures, the pattern is not doing that. So I have some more work to do to make it correct.
I am still very pleased that I managed to correct the problem. Many thanks go to Duke Thomas, Mistress Cairistiona, and Mistress Beldthora for their assistance with my attempts to fix the problem, and to Master Lorenzo for moral support.