Instead of constantly troubleshooting - backup all your data / apps with Titanium backup or some other backup utility.
Then grab the official rooted jellybean rom + Odin 3.0.7 from these forums
Reboot into recovery and nandroid backup (set backup type to .tar !!!) your current setup (just in case - you can delete it later)
Do a factory reset to wipe everything, and I also wipe cache a 2nd time and goto mounts/storage and format system too just in case.
pull the battery, put it back in and put the phone into download mode and use Odin 3.0.7 to flash the rooted Jellybean
As soon as I got my S3 I did this. I didn't even power on with whatever came on the phone, immediately flashed a fresh jellybean.
The wipes may be un-necessary since you use Odin, but may as well format everything once you have done a nandroid backup.