Hi @JamieMenshouse
Content from a course template is only added when a course is newly created. You can't use a template to add content to an existing course.
If you are an admin, you could add the quiz into Commons, then when you find the quiz in Commons, you would have the option to import the quiz into all the courses where you have a Teacher, TA, or Designer role. See https://community.canvaslms.com/t5/Canvas-Commons/How-do-I-import-and-view-a-Commons-resource-in-Can...
If you do not have a course role in all the courses and you are currently using SIS Imports for enrollments, you might want to consider whether it is worthwhile to temporarily add yourself as a Designer in all the courses, just for the purposes of this process.
However, if you do not want to do that, you might be able to use the Content Migrator API (https://canvas.instructure.com/doc/api/content_migrations.html ) combined with some scripting to come up with an automated process to copy from your course template into existing courses.