No, I don't want to break my link at all. I still haven't recovered all of the work I lost the last time that I did that, and I don't want to redo it for a third time.
The whole purpose of deleting these unlinked citations is because some of them have come up as the point of failure in my sync, and I'm doing all that I can to fix it manually.
Whenever I'm working in the person tab, I always say yes when prompted to permanently delete a citation that is no longer linked to anything. Unfortunately, that only happens when you're unlinking the citation from the last fact to which it's attached. I ended up with these 170+ unlinked citations because I deleted facts that were linked to the citations. It's too bad that you don't get the prompt then, and it's too bad that the software operates so poorly that you can't delete them in the Sources workspace without a crazy delay.
Oh, my dysfunctional FTM! When will your makers care enough about you to make you work right?
PS. If I ever get my tree synchronizing again, I will undoubtedly try silverfox's suggestion to link them all to some fact and then unlink them via the person tab so I can do it more efficiently. For now, as I've deleted the citations that have appeared in my sync log as causes of the failure, I'm leaving these 170+ alone.