For instance, this code gives me the descriptive name of the unicode element 0x1F42A, from the Symbola font collection.

Actually, that code gives you the Unicode name for 0x1F42A. charnames::viacode is unaware of fonts.

Now, following your link and following a link in there gets me the zip file. Unzipping the archive, I find a file called Symbola605.txt. In there, I find a line: "Character repertoire of Symbola", followed by a long list of characters.

I expect your answer can be found in this file. And ultimately in the file Symbola605.ttf, but that requires knowledge of the ttf format - knowledge I do not have.