Hi Andy,
Another option is to make it an assignment instead of a quiz. Sounds like these are essay questions. Check out Turnitin. I do not work for the company. We use it at our institution. There is a plugin to work with Moodle and our faculty really like the option.
Your essay questions would be an assignment that gets submitted to Turnitin through Moodle. As the evaluator you would click on submissions in Moodle and then click on the student's submission. This opens in Turnitin show redundancies/duplication. I believe you can even create a sort of bank of your students submission for the comparison basis. Grades are in Moodle. Has a lot of nice features
Hope this helps.