I got muddled where the upward-pointing triangle is as wide as its going to be and you need to reverse twist and start an up-side down triangle.
Moreover, I discovered that I was merely making something similar to Tegle. I was following Collingwood's directions in The Techniques of Sprang for a triangle of S twist interlinking on a background of Z twist, modified to include more triangles. I peered at the picture of the Tegle stocking in Hald's Old Danish Textiles (which is clearer than Hoffann's picture in The Warp-weighted Loom but still not easy to analyze) and realized that while Collingwood's direction are a good start, Tegle is actually is Z on S. I used too few warp threads in each triangle and I started the points too far to the left.
Since the points are too far to the left, the working row's first few twists at the edge are slanting the wrong way, and therefore the strands are not regularly arranged in the shed one up and one down. It's noticeable in the gap where the bone sword shows through. (It's actually a nalbinding needle used for a sword.) That's why I can't get started with upside-down triangles. I'm sure there's a way out, probably involving a row of Z twist, but the arrangement isn't working for me and I'd rather start again.
At least the embossed look appeals to my taste, despite being done in cotton yarn which I dislike.