If you copy those broken pictures to your computer, do they also look broken there? If so, I'm not sure if there's any way to recover them, since the file itself is probably corrupted.
Regarding the 3rd party clipboard app you mentioned -- it's worth seeing what happens if you reinstall the app and see if it restores that data. But I doubt it will restore what you're looking for. The data that's backed up probably has more to do with settings, account information, etc. Since a clipboard app would still be dealing with temporary data (likely stored temporarily in the app cache, not app data), it's unlikely that the data you're looking for would have been backed up.