What is the origin of the phrase "buck naked"?

The possibility you left out is that, rather than a bowdlerisation of "butt naked," it was an eggcorn of it; however, determining whether such a change was deliberate or accidental would be nigh on impossible.

Of the three, we can argue in favour of the second, though with the people referenced being as much those of African as of American origin.

We find "buck naked" in the 19th Century.

We do not find "butt naked" during that period.

We do not find it any earlier.

We do find "buck" being used to refer to men of African and of American Indian origin.

We do find the lack of clothing in some parts of Africa and America remarked upon. We also find slaves in the American South often working with little clothing. (We also find it overstated, a cartoon of an African might likely feature them as naked even if that would be highly unlikely in the scenario depicted — we're talking about people with some pretty strong racial prejudices here).

As such, we have a group of people being called "bucks" whose nakedness is often remarked upon. This suggests that the likelihood of it being the origin is quite high.

It's far from conclusive though, and you aren't going to get any better unless you hit documents from the period and manage to track it down better yourself.

I remembered reading about this subject a few years ago and I found the source:

The standard expression is “buck naked,” and the contemporary “butt naked” is an error that will get you laughed at in some circles. However, it might be just as well if the new form were to triumph. Originally a “buck” was a dandy, a pretentious, overdressed show-off of man. Condescendingly applied in the US to Native Americans and black slaves, it quickly acquired negative connotations. To the historically aware speaker, “buck naked” conjures up stereotypical images of naked “savages” or—worse—slaves laboring naked on plantations. Consider using the alternative expression “stark naked.”