Place all your questions in a question bank at a higher level. For instance you could put them at the System > Default for System level. Of course at that level, every teacher can get to them, so you might not want to place them there.
Personally, since all the courses I was involved in before retiring were in a main category of, Technology Education, with multiple subcategories and courses, I placed all my questions in the category, Default for Technology Education. That way they were available in every course I taught and since I was the only Technology teacher, no one else could "mess" with them.
If you decide to go this route, you should be able to select all the questions in a current category and move them to your new category. CAVEAT: I set mine up so long ago I can't remember for sure if questions being used in a quiz can be moved, or not, so you might have to delete quizzes, move the questions, then rebuild the quiz.