Hi Ediacaran,
Though I am one of the authors on three of the cited papers (will try to preserve some anonymity by not saying which one), I am not Svante
While I will probably disappoint you as I am a molecular biologist and certainly no expert morphologist, what I can say is that because of convergent evolution, sloth (and all Xenarthran) phylogenetics based on morphology is a mess. It is not really clear what they are. This is not really unique problem as it is still not entirely clear what the primates are most closely related to either. Another problem with sloths is that they appear to have diversified rapidly over a relatively short time period while filling similar ecological niches in different places i.e. Antillian sloths, South American sloths etc. which makes finding phylogenetically informative characters difficult ...this is also a problem for DNA based analysis.
For two morphology based analyses of sloth phylogeny there are
McKenna, M.C. and Bell, S.K. (1997) "Classification of Mammals above the Species Level", Columbia University Press, New York
and Gaudin, T.J. (1995) The ear region of edentates and the pyhlogeny of the tardigrada (mammalia, xenarthra). J. Vertebr. Peleo. 15: 672-705.
One more general reference is
Engelmann, G.F. (1985) The phylogeny of Xenarthra. in "The Evolution and Ecology of Armadillos, Sloths, and Vermilinguas" (G.G. Montgomery, Ed.) pp. 51-64, Smithsonian Institution, Washington, D.C.
Hope this was at all helpful.
Cheers,
M