Alright, what ethics system are you using to reduce questions of morality to questions of fact? Kantian deontology? The principles of Nicomachean Ethics? The Bible?
most people don't believe that [the ends justify the means]
Why do you say this? Is there a study that says that? What were it's methods? Was it a single question, or were people subjected to a series of moral dilemmas?
In my experience, most people when faced with the trolly problem will conclude you should pull the lever, so I'm very curious as to the basis of your reasoning.