I played around with copyparty and I have to say it is just awesome! The config is just fun to mess around with and everything feels snappy.
But I ran into an issue with FTP (probably just something I configured incorrectly) and could not find a discussion for that. I should probably start an issue on Github but as a non-developer I'm not sure how to do that in the correct way.
Edit: I managed to "solve" the problem. Apparently the user uploading to a subfolder over FTP needs the move permission for the folder above said subfolder.