Unfortunately, no, I’m not an expert on the taxonomies of WordPress. Nor do I want to be.

To be sure I’m clear, are you telling me it’s NOT possible to have a hierarchy of albums (or galleries) a user can drill down through to display the correct gallery of images?

If all the galleries of all the children of an album ALWAYS display, what purpose does the ability to provide a parent to an album (creating an album hierarchy) serve? I also am unable to find a way to provide a cover image for an album.

Do I need to create pages for every level of the drill-down hierarchy and only use a single level of album containing the galleries as the lowest level?