I did some inspection and experimentation, and I found that I could get the expected cells by swapping:
Face 40 <–> Face 32
Face 44 <–> Face 36
Edge (30,31) <–> Edge (28, 29)
Those numberings are based on the diagrams in the blog post.
With these swaps, it seems to make the ordering rules more consistent with the blog post’s text description. I’d still appreciate some verification, though!