Upload the file(s) as a single encrypted image file. Break that image into stripes. Store each stripe and the decryption key in a different legal jurisdiction? Not foolproof but it does make it more difficult for a single entity.
If you do that, how is the site supposed to publish your documents in the event of your death? They're going to have to get access to the data so they can do the job.
You only do the uploading of the image. The service does the striping and jurisdictionally diverse storage.