On the one hand, I admire your willingness to dig into this. On the other, I think you are too quick to conclude that the absence of evidence is evidence.
As for "powwow dancing doesn’t entrench and authenticate a constructed Native identity anyhow", I agree to a degree: it does indicate a cultural connection. Do you think Native identity is primarily racial or cultural?
Before you answer, remember that "race" was created by Europeans a few centuries ago, and some Native Americans adopted it as a practical measure, but historically, tribal identity is cultural, not racial.
Since we're talking about the Cherokee, I'll add that I believe the Cherokee were wrong to exclude black Cherokees from membership while admitting Cherokees who knew little or nothing about the culture. (For readers who don't know about that: https://en.wikipedia.org/wiki/Cherokee_freedmen_controversy)