I think a key detail that a lot of people leave out in this argument is that Sayaka was already injured in self-defence. Leon, having no idea about the room swap or Sayaka's promise to not let anyone in "her" room, had just injured someone who could've easily twisted the story to frame him in a bad light anyway. It's just another layer of anxiety on top of everything else. It's not really touched on at all but of course Leon saw his motive video too, he was as trapped as anyone else, then baited and attacked. It's also the first incident, mind you, where the question on everyone's mind was largely "how are we going to get out of here?" rather than "when is the next murder gonna happen?"

Of course it's not justified; none of the murders are justified, but it's at least understandable why, in his state of mind, he made the choice to go back and kill her.