Have you ever heard of a case where the only skillful thing for the teacher to do was to obviously have sex with their student?
No I haven't. Like I said, our teachers made it clear that in our tradition physical sex isn't used as a method. This is pretty accepted Nyingma and Kagyu since it's been an issue in the west.
How many cases of abuse, or "questionable" cases, do you see as permissible so long as we don't know that it's a widespread issue?
By questionable I meant that we don't know all the facts and the courts never decided anything conclusive (that I know of). If we know there's abuse then I would say zero cases are permissible.
How can we know for sure whether a teacher is recommending karmamudra skillfully or to satisfy their own base desires?
Good teachers in Tibetan Buddhism don't get their reputations easily. This is why we don't see many western teachers in Vajrayana, it's a very strict sort of training and recognition. Those like Geshe Roach who do get the training and proceed to abuse their position are quickly denounced.
Do you feel there should be a list of Lamas who are deemed qualified to have relations with their students so that their students know it's possible while also suggesting that students of other teachers err on the side of caution (stay away from such practices)?
Again, I don't know of any accepted teachers using this method in their body of teachings. If a lay teacher and a student decide to have a relationship then that's their choice but it's not part of any cycle of teachings that I know of. There are very effective practices in Anuyoga as the Dalai Lama said, there's really no need for this stuff. I do think we can be careful to harness the sexual energy rather than suppressing it. Suppression can have perverted results.
I think there's enough material out there in plain site for a student who might be confronted with this sort of thing. As people on reddit, many of us don't qualify as rape counselors or realized gurus so I don't see any benefit in expounding the issue. As /u/HeartOfTuxes mentioned, ngondro and other preliminaries come before Anuyoga so ideally the student would have a stable and somewhat realized mind, leading to much better judgement for any situation they'd encounter.