Actually moving the questions to the system level will make the issue worse, not better. With the current design, when the quiz is included in a course backup it includes the entire question bank up to the system level. This means that if you move all the questions to the system level, they will now be included in every course backup that has a quiz regardless of whether the questions are used in that course or not.
If you want to avoid huge course backups, then keep all your questions at the course level.
However, I would also advise you to upgrade as overall Moodle performance has improved greatly and we are not seeing near the issues with backups as we used to.