This is Dr. Margaret Walker (wiki bio poetry selection). She was born in Alabama in 1915, went to school in New Orleans, and worked as a poet and professor right up until her death in 1998. Her take on Stag was originally published in 1942, when Walker was still a young woman, recently employed by the New Deal's Work Progress Administration and its Federal Writer's Project (alongside Richard Wright). This is a transcription of dialect, and Walker reads it as such in both recordings below. (Both source albums also include recordings of Walker's poem about "John Henry," another legendary black American story also told in dialect.)
Walker recorded her poem twice for Folkways, the record label that also released Harry Smith's epic Anthology of American Folk Music, and a lot of the recordings of Woody Guthrie, Pete Seeger, and Leadbelly. The first time was in 1954, twelve years after she published the poem -- at the time she was living in Jackson, Mississippi with her husband and their four children. Twenty-one years later, she returned to Folkways to record three albums, one of which included her poem about Stag.
I've included both of them here, so you can hear how the two versions are different -- the text is identical in both, but the delivery varies. The first one is faster, and Walker makes the cartoon birds flying around the cop's head funnier. The second is clearly the voice of an older woman -- this version spends a little more time (going a little slower) when we hear how Stag escaped the lynching meant for his hide, and the tale of how Stag haunts New Orleans.
Walker is pretty important as far as poets go, and this post clearly hasn't done her justice -- click on that poetry link at the top to read more, or go down to the buy link and support the work of Folkways while listening to more from her.