Morwen,

In the U.S., "pickaninny" does not (/did not) just convey the meaning of "Black child." The "pickaninny" represented a specific type of symbol / trope / meme / whatever in racial imagery—a symbol employed in various yet often specific ways.

For example, one might want to evoke certain racialist ideas of Blackness without evoking others. I don't really want to get into that world of thinking and its demented "logic." It suffices to say that I think people who used the quip about Berlin were adeptly (if that can be said) using the racial language to convey what they wanted —the idea of an essential Black character/ way of being/ musicality/ etc— without any extra unwanted connotations and within prescribed ideas of what one could say so as to not be perceived as "a racist" per se (while of course still subscribing to ideas about race).

My last sentence was a long one so in brief: My opinion is that while "pickaninny" (or "little colored boy") is rich with connotations, I doubt that in the context of the quip there was any intended meaning re: Berlin beyond the one "Berlin is a White man amazingly adept at capturing Black musical style."

I think your various interpretations are well thought out, Morwen, and interesting. Could be; they don't ring especially true to *me* though.