I would like to suggest adding a flag to the Advanced Translator that toggles when the user presses the "copy source" button. It would probably be nothing more than a hidden input field and a line of JS code.

When the post is saved and translations are updated/created you could then use that info to perform an "initial sync" of post data (Attachments, Shortcodes, Post Meta, ...). It does not make sense to do this for every single post update because users may choose to manually overwrite the results afterwards.
#140 might already allow us to do many of the suggested actions, but it certainly cannot hurt to have this little piece of data available when actually saving the post as well.