In addition to those suggestions already offered, there is also automated course backups which will use backups preferences set in site admin (ie, you), and make a backup of each course (if it can). Suggest, if you do this, send to a 'designated directory' that you as admin must manually create and do pick the destination/location on a partition/drive that has plenty of free space and outside of moodledata.
7 years worth of course usage ... courses could be in fairly bad shape ... teachers could have opted to hide an activity as opposed to removing which could mean there could be a lot of 'junk' in a course.
By chance would you know what course is the largest in size - maybe most used?
Have you polled your teachers to see which ones might not want a backup?
Before you begin embarking upon this, do make sure you have a full site backup - code + DB + minimal moodledata/filedir/