I have a jailbroken iphone 4 with 5.1.1 and would like to upgrade to one of the 6.x.x versions. From what I've been reading this seems like an impossibility.
Is there a way, or should I wait for a 6.1.3 jailbreak?
You can get a tethered jailbreak on 6.1.3 on the iphone 4. If having an untethered jailbreak is important to you then just FYI there will not be an untethered jailbreak for 6.1.3. No one is working on it. The jailbreak devs have shifted their focus to iOS 7.