You overlooked the fact that TinyUmbrella cannot help if you did not happen to use it to collect your iOS 5.0/5.0.1/5.1/5.1.1 SHSH blobs generated uniquely for your device by Apple at the time that iOS 5.x was the latest version available. Once iOS 6 came out, if the blobs for previous version(s) had not already been collected, then it's "tough luck: you're stuck."