Sorry for the resurrection of this old post.
I too have been looking into wood ash as a clay substitute and mortar binder.
Here is a video by Primitive Technology on wood ash bricks:
https://youtu.be/DP0t2MmOMEA
Ok, here's my thought...
Sift the ash for fine particles and much less organics. Wet it and mix, and drain like in the video. Instead of refiring it, add straw for a cob-like mix. You could also make the mortar out of it to build a stone based rocket mass heater and the ash-cob as a covering.
Thoughts?