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You may solve the conundrum by using Uploadcare, it can help in situations when you have little or no control over host filesystem (GAE, heroku, shared hosting or whatnot). Uploaded files will be stored in Uploadcare and you will store file UUIDs or URLs in your DB.
There is Django package: pyuploadcare
disclosure: I am one of Uploadcare developers and am posting this not to shamelessly promote the service but because it was built to solve cases like this one.
Source:stackexchange.com