I figured it out:
to do this change lines 50 & 51 in the plugin file 'slideshow-gallery.php' to this:
add_menu_page(__('Slideshow', $this -> plugin_name), __('Slideshow', $this -> plugin_name), 7, "gallery", array($this, 'admin_slides'), $this -> url() . '/images/icon.png');
$this -> menus['gallery'] = add_submenu_page("gallery", __('Manage Slides', $this -> plugin_name), __('Manage Slides', $this -> plugin_name), 7, "gallery", array($this, 'admin_slides'));
The number (', 7, "gallery", ') denotes the level of user who sees the admin menu. It was set at 10, which is admin only.
I'd imagine it's very obvious to plugin writers - but it wasn't to me! Now I just have to remember to edit it when I update the plugin.