Erasing iPhone, Not Restoring from Backup, Keep App Settings?

[yanathin]

I'm in a bit of a predicament... My iPhone 4 has been acting up lately. I took it to the Genius Bar and they informed me that there are a few files that are corrupted, and the only way to fix it is to completely erase my iPhone and to NOT restore from a previous backup (which will just load the corrupted files back on there). Is there any way to do this while still being able to keep app data for a few specific apps? There are some apps and games that I would be devastated to lose all of my saved data for. I noticed that in iCloud's backup settings you can select which apps to back up data for, but I didn't find any toggle for "system settings" or anything like that. I'd really appreciate any help on this issue. Thanks!!!