Paul Bunyan is part of a tangle of vague origins, modification and distribution in print, and character assassination by one of America's early leading folklorists. I have not published on this, so I am relying on the sources I can find, but I can provide some academic context for what is going on here.

The leading problem with this cycle of stories is that they were promoted and adapted early on by an advertisement campaign. Paul Bunyan became the beast of print and literary invention. There was a cycle of Paul Bunyan stories in the oral tradition of the old Northwest of Wisconsin. This was "grabbed" by the Red River Lumber Company with a promotional pamphlets published in 1914 and 1916. At that point, the oral tradition faded into the background and literary adaptation and invention took over. What remains is a complicated mix of natural, artificial and processed elements, resulting in something akin to "Wonder Bread": that is, it's a wonder they call it bread since it seems little more than processed, semi-edible material that is reminiscent of bread.

Because of this, noted early American folklorist, Richard Dorson (1916-1981) asserted that Paul Bunyan and his stories were "fakelore" and should be scorned, ridiculed and discarded as the sort of phony literary bastardization that confused people about what "real" folklore is all about. That horrible term, "fakelore", is Vampiric in the way it refuses to die even thought it has outlived its usefulness and carries with it a dreadful amount of ill-conceived judgment.

The fact is, since people have been writing, they have borrowed from oral tradition, and conversely, what they have written has affected oral tradition. This is nothing new, and if we were to wish this away, we would only be successful if we disposed of literacy. Try as America might in this regard, even the great USA is not likely to be successful in becoming a (totally) illiterate nation. Literature and its entangled relationship with oral tradition is here to stay.

A break-through collection of articles edited by Michael Dylan Foster and Jeffrey A. Tolbert, "The Folkloresque: Reframing Folklore in a Popular Culture World" (2016) offers a way to sort out this tangle. They replace the pejorative term "fakelore" with the neutral term "folkloresque," suggesting that there are things in a literary society that recall the nature of folklore, imitate or borrow from it, and seem like folklore, but really aren't. As they say in their introduction:

If folklorists study people (+ folk), then it is critical to explore what people think of as folklore - regardless of how a folklorist might categorize it. Even if Disney, Paul Bunyan, or Dorson's "claptrap collections" are not classifiable as folklore (by a folklorist), they are certainly a form of popular culture that people identify with folklore - exactly what we are calling the folkloresque. (9)

No one should be in the position of judging what elements of a culture are good or bad. Culture is neutral. It is clear that with literacy, cycles of stories - or just isolated motifs - emerge that seem as though they are direct reflections of oral tradition, but they are more or less literary invention, and whether we regard that written document as a delightful homage or a crass exploitation is irrelevant.

It seems there were some stories about Paul Bunyan circulating before 1914. I'm unclear about how well collected these were, and I'm not sure any amount of digging will be succesful in putting a lot of focus on the nature of the cycle of stories because whatever that original cycle of stories was, it was overwhelmed by the power and flooding effects of the written word. After 1914/1916, the world of the printed word took the cycle, rewrote it, and redefined it. After that point, it reentered American folklore, in a way, simply because people believed it was part of their national folklore legacy. It became, as Foster and Talbot would say, part of the American folkloresque, a cultural element that was entwined with the written word, but regarded popularly as part of American folklore.

This site is helpful in providing details.