There are too many examples of oral history matching historical events for me to bother being your Google here.
Very little weight has been given to the accuracy of these oral histories until recent times. Meanwhile tribes have been saying “that’s not how it happened” to the Clovis hypothesis the entire time.
I probably don't need to tell someone like you who's intimately familiar with them, but for others reading oral histories don't work like the literary histories we're all familiar with from textbooks. What's preserved has some fairly consistent modifications that take place on the journey from the top of the hourglass to the bottom of the hourglass and into deep time histories.
1) Events become omitted, repeated, or conflated to support the narrative purpose of the tradition
2) Elements of the narrative that support the narrative purpose are emphasized or modified to better suit that purpose, sometimes at the expense of modern ideas of historical accuracy
3) Elements from other narratives that support the narrative purpose may be incorporated, or supplant other elements within a tradition of parallel narratives.
4) Elements that are dramatic and narratively meaningful are the ones that survive
These are more or less basic knowledge by anyone working with deep time stories, but if you insist on an indigenous source here's a paper by Roger Echo-Hawk saying the same thing much more eloquently: https://doi.org/10.2307/2694059
So, to use these stories in academic work we typically have to find some way of matching the narrative echos of the real historical events to the things that are visible archaeologically. That's incredibly difficult beyond a few hundred years, and tends to center around dramatic events like natural disasters and geographic features. Well, we don't have many of those for the LGM. Past work has usually centered around identifying either "Dark World" motifs with Beringia Standstill populations (the BSH is incompatible with the White Sands timeline), or Diving Bird myths, which are shared with many Eurasian groups. I'm not aware of any feature of Diving Bird myths that would allow a timeline for the initial peopling, hence the question.
> In conceptual terms, scholarship on the past should revisit the bibliocentric assumptions of “prehistory,” and pursue, instead, the study of “ancient American history”-an approach that treats oral documents as respectable siblings of written documents.
Though, in that same vein is another semantic paper called something like "Rehumanizing Pleistocene People", can't remember the author with bad Internet.
Edit: Also thousands of historical written documents that are disputed or tossed aside.