You don't mention what version of Moodle you're using?
I can only speak for 1.9x. If using the Questionnaire module you might decide to use a "Public" questionnaire. What this does is have all results accumulate to the course from which the public questionnaire originated. Instructors with access to that course would be the only ones able to view the results. A download to text file, opened in Google Spreadsheets (or, Excel, if you have to) would tell you from which course each response originated and allow you to aggregate your results anyway you want.