Unless the developer of your app ignored all Apple programming standards a backup does include the data in your app's files. For several persons that are in your situation they have found that they can access their data from their backup using a program like Backup Extractor. If your developer created some sort of proprietary formatting then you are correct, you would not be able to get them but I doubt this is the case. Give it a try.
So you admit you saw all the warnings? Including the one where they said your app would no longer work? I think for any reasonable person that would include the fact your won't be able to get to your data.
The only short sighted person in all of this is you. You were given several warnings and you did absolutely nothing with them. A word of advice: when you check engine light comes on you should do something about it.