I'm posting a follow-up on this topic. It took four years but I found her! The Native American lady who was the subject of my pyrography mirrors appears to be from a 1902 painting called simply "Indian Squaw" by Elbridge Ayer Burbank.
Here is the Indian Squaw painting and the portrait on my mirror:
And for comparison so that you don't have to scroll back, here is the portrait previously ID'd as Wolf Robe and his photo:
Here is the whole mirror: