I've not found an app that will help you out. The apps available appear to help out only with retrieving files from your synced backup - and you say that you don't have one...
There seems to be other apps that are mentioned on some sites promising direct recovery from iOS devices - that are just promised "Coming soon!"
If your data is really important, you could contact Drivesavers to find out what they charge for that.
Maybe someone else may add good info, but I don't see anything promising for your situation.
Serendipity is a lucky guess !