You don't have to tell me how oral histories are preserved. I've worked as an anthropologist and documented some. What I was asking is how you operationalize what
is preserved to distinguish between the various competing hypotheses for the initial peopling of the Americas and which histories you're referencing.
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.