What way out? You do realize that the vast majority of individuals don't have the magical plot armor that is being friendly to the games main character? They ain't getting out. Their life is over. If getting out of slavery was even remotely common than the whole system wouldn't work to begin with.
And that's the point I am making here. For the absolute supermajority of individuals the only thing a calm, polite and sensible approach would do is give them time to react and either try to run, defend them self or do something else to try and desperately claw their way out of the situation or die trying. And from the perspective of the captors that's a liability at worst and an annoyance at best.
That is why the response the hospital had is actually quite reasonable. They want to overwhelm the victim with rapid concentrated force so as to ensure it newer gets the chance to do react.
Now it's horrific to look at and experience to be sure. But it makes sense from their perspective.
You skipped over the part where Maria has people on the outside that would do anything and everything, including violent action on Nia's part, to get her out. She would get out, the only real question is how that would happen, whether it was all out war or diplomacy. This isn't about most people, again, I am taking this specifically from Maria's point of view because she was the one held. There is no majority or supermajority involved, it is one very specific individual.
The response the hospital had is in no way reasonable because, again, they risked damaging their prize and wasting the effort. If she then ends up getting no buyers specifically because the overkill response injured her beyond any recognizable value, she is then useless to them and she might as well have been treated as if she were human in the first place. It would get them the same value with less effort and less expense.