You can't do this using a Drag and Drop quiz because, as you say, each drag item can have only one target. To make it work, you would have to create it from scratch.
It can be done, easily enough for one teacher, but I have questions about what happens when you add a second teacher, if I am understanding the description correctly. To make already chosen sections disappear, or unavailable, you would have to have open the project on only one computer, and keep it open for all the teachers.
I would use a spreadsheet on a shared drive. Create as much description as needed, 12 time slots, and let the teacher enter their name in the appropriate places. I don't think it can be done in SL, and would take days if it could. In a spreadsheet; minutes and printing it is already built in..
Personal rant: Drag and Drop is very alluring, appealing, and glamorous, but has some serious drawbacks. It doesn't always work well on touch devices, and isn't disability friendly. Users with lower tech skills may struggle to figure it out, while almost everybody can enter their name. I love the idea, but don't use it.
P.S. The file didn't attach. Be sure you use a browser, and not a phone to attach it.
