Forgot to add ... since the students are already enrolled in courses, at present, setting the roles of students that have not paid to 'non-paid' role at the sysetm level may not have desired outcome (those students now have two roles - student and non-paid student). If they are already in a course, their role is 'student'.
However, teachers should be able to re-assign students in their courses from student to non-paid student. They do need, however, some way to get a pdf file from the student that shows they paid (or something like that).
Yes, I know that means work, but one is having to un-do what has been done and know of no 'magic bullet' at this point.
Once having setup this role and having that role as default (rather than student), then next years process will change somewhat, but you won't be where you are at right now ... having to un-do then re-do - staying with core/non-hacked Moodle code. This would also be true of any new courses (I think!).
Setting up a guest course - "Having Troubles?" - or some sort of title that fits, even non-paid student roles can see a label. In that label one could provide information about how to correct their role and gain access to courses for which they've paid.
'spirit of sharing', Ken