Another idea, which may require too much effort on the part of the user, is to show a unique token or url for each uploaded piece of content. The user can choose to store this and use it to edit the content.
Advantages: it's more anonymous, since there are no cookies to track users, and you can't even track which pieces of content are uploaded by the same user. The tokens also persist after clearing cookies or even reinstalling the PC.
Disadvantages: it's clearly quite some effort for the user to keep track of all the tokens.
P.s. it sounds like may use your service to upload nsfw or copyrighted content.... But maybe that's the point.