This doesn't help with your attribution but as you likely know, the Yomud Turkmen also use the "bird-on-a-pole" design in their pile weaving, usually as a border but also sometimes in the field.

Jerry Thompson has a tent pole cover in the Jon Thompson-Louise Macke catalog that uses it in the field.

The Yomuds use this device with one "wing" forward and the one back, as in your piece, but also with both wings back.

Technically, a "tessellated" design is one that covers the entire field without any gaps or overlaps. Some diamond designs qualify. The "bird on a pole" instance is a somewhat more complicated one. You might not realize at first, looking at an isolated instance of it, that it was capable of a tessellated application.

Interesting piece.

R. John Howe