Automated individual application backup for iOS applications without jailbreaking?

Last week, my 6-year-old lost a Minecraft Pocket world / save and was devastated because our last iTunes backup was from before she created it, and our last iCloud backup was made since the world was deleted, and as far as I can tell it looks like the iCloud "backup" is a snapshot of the entire filesystem at the time it's made, with no history.

So, the Apple-provided backup mechanisms failed me. They're not granular enough and don't keep a history of file states. I need to back up individual files.

I just found out that it's possible to access (portions of) the filesystem on an iOS device without jailbreaking, using desktop applications like iExplorer and iFunBox. This is great, because I can back up the data in my applications manually. The problem is that, since it's a UI, I can't automate the process to make a regular, periodic backup. I have to make a new backup by hand, every time.

What I really want is basically Time Machine, for iOS application data. I don't expect that level of polish, but I'd like to be able to use whatever mechanism is used by iFunBox to talk to the iDevice filesystem, ideally from the command line, which would let me script backups to occur on a regular basis. Failing that, an application like iFunBox that automatically backs up specified apps' file data would be great.

Is this possible? Is it being done today?