Multiple galleries - can you edit the display page for each gallery individually?

This is by design, yes. When editing the page, you're editing it for the Group Theme - in other words, you're editing the (for example) "Gallery - Home" page that will be used for all galleries in the group. Theming is intentionally content-agnostic in this way.

To accomplish your goal of some unique content in each gallery, you could use an existing field, such as the gallery's Description (editable via Manage Gallery > Gallery Options), and modify/create a widget to get the current gallery and display that field programmatically.

Thanks. I'm using the Tag Cloud, which does adjust based on the items in the gallery, and we're using another method to provide an index. Appreciate the context!

Thanks. I'm using the Tag Cloud, which does adjust based on the items in the gallery, and we're using another method to provide an index. Appreciate the context!