As Oestreicher points out, Rafinesque was pretty bizarre by modern standards, and most modern scholars worked with Brinton's translation, and that's what I did as well.
The major problems that I have with Oestreicher's analysis concern:
1) the Lenape mede/wak - whose existence and operation are well documented.
2) the Lenape migration, and Oestreicher's interpretation of it - I suppose I'll have to make this as easy as possible for you, and to give others a warning as well:
For a discussion of the appearance in eastern Wisconsin of Oneota culture, see Victoria Durst, The People of the Dunes, Whitefish Dunes State Park, 1993, p. 46-63. For a discussion of the appearance of Oneota culture at Redwing, see Clark A. Dobbs, Red Wing Archaeological Preserve, Goodhue-Pierce Archaeological Society Planning Committee, Institute for Minnesota Archaeology, Minneapolis, 1990, p. 7. For a discussion of the western Oneota culture appearance and distribution, see James L. Theler and Robert F. Boszhardt, Twelve Millenia, Archaeology of the Upper Mississippi River Valley, pages 152-155, particularly abandonment of effigy mounds, p. 155. In their book on The Gottschall Rockshelter, Robert J. Salzer and Grace Rajnovich cite cannibalism at Aztalan, citing Fred A, Finney and James B. Stohlman, The Fred Edwards Site, New Perspectives on Cahokia, Prehistory Press, Madison. One problem assigning this here to a climate collapse is Oneota occupancy at Aztalan, following on the Stirling phase occupancy at the site. For carbon dates at this site: Lynne Goldstine, Joan Freeman, Aztalan State Park, Wisconsin Department of Natural Resources, 1995 for group burials and stockade history.
For radio carbon dates for the stockade and later fall of Cahokia, see the literature. For the radio carbon dates for Angel Mounds, see the literature. For "Middle Fort Ancient" sites in this area, see the literature - but note that "Middle Fort Ancient" attacker and defender sites are seldom clearly delineated. In this regard note especially the Ana Lynn site on the Blue River in Indiana, rc 1170-1270 CE, for evidence of the Lenape flanking move around Cahokia ("Twakanhah" in Iroquois, "Towako" in the Walum Olum) and their recent defeat of a Mississippian people on the Ohio River.
For the east central areas of North America, the "Wellsburg" complex appears to be equivalent to Oneota. It goes by a yet another different name further east in far Western Maryland and central Pennsylvania...
Aside from the archaeological sequence given above, you have the Missasagua, Assinapi (Anishinaabe?), Mengwe (apparently Siouxian Monacans in this case), Towakon (Twakanhah, Cahokia), Tallegewi (Tchilagathawi), Talmatan ("Neutrals"), etc. all showing up exactly where they were in the WO. How could Rafinesque have guessed all of them correctly? Heckewelder didn't mention them.
Another really stunning coincidence for me is the burning of the stockades described in the WO, and if CSR dreamed this up 150 years before the stockades at Cahokia and Angel Mounds were excavated, then one would have to admit he had an unbelievably great creative talent.
3) the Lenape deluge tradition - whose existence is independently attested to by Heckewelder and Zeisberger.