Many thanks, Alan!
That makes it much clearer. After reading your reply, I examined our setup more closely together with our Archivist, who explained to me the process she uses to submit the Theses. Turned out that she puts everything into the main Graduate Theses collection and then maps each item to the collection of the department where the student wrote the theses. So, each item has two entries like this:
Graduate Theses
Department of Education - Graduate Theses
It's just that for the Applied Human Nutrition items it looked like this:
Graduate Theses
Graduate Theses
Thanks to you, we figured out that every thesis is mapped, we just needed to rename one collection, so we now have:
Graduate Theses
Applied Human Nutrition - Graduate Theses
And, of course, as you point out, the Handle links do not change, so we are golden! Another crisis averted :)