It appears that Harry is dead set against AKing Umbridge, because it would make Voldie happy for him to do so. Which raises the question: how is Harry going to try to remove her if he's not willing to kill her?

Because you know that now he's got this knowledge he's going to come up with some damnfool reckless plan (unless Draco manages to inject some cunning, or the rest of the ISS manage to pull off an assist).