Some of those old recordings are really low quality to start with. There are a couple of maybe unprocessed tracks from 1899 on the "Ojibway Music from Minnesota" CD that the Minnesota Historical Society released in 1988. I'm not seeing it freely available anywhere but it looks like at least last.fm has a page for it (however the CD only has 15 tracks and they list 20, not sure why...). The 1899 tracks are the two by Swift Flying Feather, "Moccasin Game Song" and "Love Song" (not the others of the same names on that CD that are from the 70s and 80s). The track "Dream Song" by Kimiwun was recorded by Frances Densmore in 1910 and is much clearer (the "Women's Dance Song" by Ponemah Singers is a 1972 version of the same song from the same community). They are all excellent songs. I can highly recommend the whole CD. According to the booklet there were also 6 recordings of Swift Flying Feather made in 1869 by Alice Fletcher. I'm not sure if those (or any other of these old recordings) are available anywhere. Edit: The page I link to below mentions these as being 1899 so I think the 1869 was a typo in the booklet and the two Swift Flying Feather tracks on the CD are the recordings made by Fletcher in 1899.
I think this page is a small part of the text from the booklet that came with that CD:
(I don't want to click around the podcast version of this story just to hear short snippits.)