How about treat saved data as files (slots) stored in cloud or local storage.
Open: player opens his local files menu and pick one file to play it
Download: player opens his cloud files menus and pick one file to download it into a local file.
Upload: player uploads a file from local to cloud
New: player initials a file in local
Player only could see his local files menu if off-line, and he could download or upload files if on-line.
Local file won't be overwrote until player download a file from cloud.