Currently it is not possible to display the contents of a Photo Album onto a page as if it were an Image Gallery. This is unfortunate as, in my experience, maintaining a large Image gallery in its shortcode is CPU and RAM intensive and does not perform well on servers with limited resources whereas the Photo Album custom post is MUCH EASIER for my clients to edit and maintain. Plus an album is easy to reuse where ever you want to place it.
MY SUGGESTION IS TO ADD A FEATURE TO THE IMAGE GALLERY SHORTCODE …
to select a source feed for images to be either a specific photo album post or photo album category!!!