by Ken Task.
Not sure I can help further ... error log files ... do you see any lines that say 'MySQLServer has gone away'?
That's usually an indication that max_allowed_packets setting is too low. If you cannot tweak that upwards, the only thing one could do is break apart backup and restore in pieces.
Without ability to tweak variables, both PHP and MySQL ... would probably fail considering a rather large questions.xml (question bank for quizzes/test).
Could try backup with nothing but quizzes and not all of them!
'SoS', Ken