iCloud Restore Fails

I have an iCloud backup of my iPhone 4 that I'm trying to restore to my new iPod touch, 5th generation. The backup was created in March, 2012, when my iPhone 4 was stolen. A few months ago, the iCloud backup of my iPhone 4 restored successfully to an iPad 3 (which was iOS 5 at the time).

But apparently this backup is not compatible with iOS 6. It does not error when I restore it to my new iPod touch, but none of the apps can launch. A handful of system settings came across, like the name of the device and general settings.

After the restore, in order to get the apps to launch, I have to delete/reinstall them. So I know something was written to each application's sandbox.

I know the backup is good because it restored to the iPad. I suspect the backup can only be restored in iOS 5. I know I can't downgrade my iPod touch to iOS 5. I attempted to downgrade the iPad 3 to iOS 5, but iTunes refused to do so.

I guess I need to get my hands on a device that is still on iOS 5.

Any other suggestions?