There's no way currently to have attachments go into a file gallery. What you could do is go to Admin Home -> Wiki -> Features (tab), turn off Attachments, and then turn on Pictures and Use File Galleries to store pictures. This way, when users edit a wiki page, they will see the icon in the edit toolbar which allows them to upload an image to file galleries.
Using user permissions (ie allowing users to upload to and view galleries but not create them) and file gallery settings (ie whether they are public or not or visible to non-admins) you should b able direct users to a single gallery.
Not sure if that helps, but just one idea for a work-around.