Under my current view I would argue that it's the threat itself that is immoral and not what it is being used for. I guess this would draw a line between blackmail and an ultimatum

So two issues here. First, that means you don't get to draw a line between "tell your wife or I will tell her" and "if you don't give me $1k I'll tell your wife." Which I think is a pretty big distinction. Second, what about your previous concern about grades-for-sex? If a TA tells a student "You failed this test, but sleep with me and I'll give you extra credit", is the moral difficulty just the undeserved extra credit? (Equal morality to giving extra credit to the kid whose mom just died?) I think you actually consider the TA to be infringing on the student's right to bodily autonomy. It's not impossible for her to say no, but pressure of that kind nevertheless infringes on that right.

If they are making it impossible for you to express those rights at this moment, then that's morally wrong

I really don't love this - I'd like to be able to say that you have lost free speech if I forbid Democrats from using megaphones but not if I forbid everyone from using megaphones near residential areas between 10PM and 6AM.

so yet another aside. I understand that this is not a perfect illustration for what's going on but it comes to mind. Are you familiar with the Sorites paradox or the paradox of the heap

Yes, and I do not have a unified solution to all of those. Sometimes I feel like you have to draw an arbitrary line somewhere, and sometimes I feel like there is a gradient.

So my last desperate attempt at something is: would your moral obligation to help her be any different if you didn't convince her to use the log but she did it on her own and you said nothing? What about if you tried to talk her out of it?

I think so, though I've stacked so many intensifiers on this that removing one or two leaves me with what I'd consider an insurmountable obligation.

I'm putting forward that that variable, your involvement is irrelevant to the the value of your moral obligation to help (again, provided you didn't intend on the bad to happen)

So for example, a surgeon sees an annoying patient with an infected knee; does he have to schedule that patient and listen to his inane chatter or can he say "find some other doctor". If the surgeon had just done a joint replacement on that knee (so the infection is likely his fault), I think that absolutely changes the surgeon's moral obligation to take this patient.