That was a Duh! kind of moment. So easy, why didn't I think of it? (I never had explored the backup and restore functions before--way down on my To Do list--it was about time--so I did not know you could restore one course into another course.) At least now I can have users enroll into a course as soon as they pay for it, and can have them all in one place for announcements, etc. Before I felt like they were just dangling out in space somewhere until I let them into the course the first day.
My problem had always been the one of overlapping courses. Now I can make the new "empty" course named something like: Course Title - July Session, then on the day classes start I can restore Course Title - May Session into it.