You could actually do this with a group sign up plugin.
Create the course, then create separate groups for each teacher. It will be a little complex as the activities will then need to be created separately for each group with different due dates (or perhaps you could use overrides to do that part).
You could then name each group by the time frame and install a plugin (look in plugin database for this) that allows students to sign up for groups.
This way, the students can all be enrolled in the three courses that they need and then just sign up for the correct time frame within each course.
You need to look in the documentation at groups/separate groups. The teachers will need a role that does not have the see all groups role so that they only have to deal with their students - see roles/permissions. Then look at user and group overrides/restrictions for making sure that the activities are correctly dated for each group.