I've got the same problem like Jussi and i tried to set up a system with the himuesgallery module, the upload via ftp works great and you can build a folder system.
I tried to integrate the image folders in Drupals Private Dir and the result is that i can't see any picture anymore ... may i configured somehing wrong, but this seems not to be a solution.
May a module to restrict access to another folder help.
A long time ago i tried the media module and there was some other problems...
See also the Media Issues or the statement of the authors:
Private files: There are several issues in Media and Drupal core when the private file system is used. While these issue are being investigated and fixed, the use of the File lock module is highly recommended.
So my answer is: No, there is currently no working gallery that reachs your aims.