Hi Emma,
Most of my problems with Quiz backup/restore/import relate to the categories used the the Question Bank. If you use Question Bank categories above the Course level category, backup includes all of the questions within that category, even if they are not used in your course. We had all of our questions in System level category, in order to enable sharing of questions among teachers. This resulted in a test case of one course with one quiz and one questions having a backup size of close to 1gb. Impossible it seemed. This is an old bug that has plagued us going on for five or more years, with Tim and others saying it is very difficult to fix (recently, a checkbox was added to exclude the question bank from backups but this does not solve the problem when your course contains a quiz). I am hoping that Moodle HQ might put more time into fixing it if we vote on these two Tracker Issues : MDL-12403; MDL-41924.