Hi Mathew,
FYI MDL-28261 landed into the 2.7 version and, probably, will land in 2.6 and 2.5 too: please follow MDL-44913.
HTH,
Matteo
Hate to raise this thread back up again, but would https://tracker.moodle.org/browse/MDL-44913 help with recovering from the 301 LMS Not Initialized? Only way I've found so far is to manually wipe the user's attempt on the admin side.