While idly searching for more information on diamond twill fabric, I found this article about diamond twills used for the skirts worn as Lithuanian folk costume during the late 19th and early 20th centuries. (Pearl; have you seen this article?)
The authors examined 257 skirts for the article. 55% of the skirts were simple plain weave (by which I assume the authors mean "tabby"), and only 24% were twills. (The rest were either combination weaves or satin weaves). Of the twill weaves, in turn, 41.6% were 2/2 twills; only 15% of the twills are diamond twills, and it's clear from the weave diagrams that appear in the article that many of the diamond twills are not simple broken or unbroken twills but odd, unusual variants that would not have been seen in the Viking Age. On the other hand, the fact that diamond twills are a minority of the twills found is pretty much the same as in Viking Age Scandinavia. (Though I believe tabby weave was less common in the Viking Age than in this sample of folk skirts.) Most of the skirts were wool, though I recall one wool-cotton blend being mentioned.
It's an interesting little article, and I commend it to the attention of any Baltic costume enthusiasts and weavers who read this blog.