We don't have a one button solution for it yet, but backup of the database has all the URLs to user media uploads, so it should be much easier and faster to run script that just iterates over JSON with URLs, than crawl/scrape the website with all the performance and security implications of that (most likely scraper IP will get throttled and subsequently blocked by out anti-DDoS protection within Amazon WAF).

JSON contains a lot of data so I would recommend using jq to limit data that downloading software will work on.
Having JSON with only URLs and ID of the row/record that it is associated to, simple node.js script, or bash with curl could be run on a server with fast connection. If the backup is meant to be done periodically, it can be run in crontab to automate things.

Of course it is not ideal and we are thinking about ideal (secure AND easy to use, which is often don't go hand in hand) way of providing backups for both assets, and user uploads. It is on our radar, and we internally have backups guaranteed, but exposing sensitive data (which user uploads can contain, including medical) has to be done with utmost care for security - there is no room for errors.