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These files are encrypted and only you (and Dropbox) have the key. You could download these files to anywhere and hope that when you tell Dropbox to delete them from its servers, that it actually does so.
Dropbox has an API available through e.g. Python, which you certainly could use to transfer files. My thought would be perhaps to create a virtual machine on AWS, attach some storage to it then run your Python script for Dropbox on that VM instance.
