With due respect, you're begging the question. You've got a hypothesis (which I suppose is a fine one to have), but then making assumptions about something that is far from proven (which, to your credit, you acknowledge).
I really think you're underplaying the mental aspect of it in an attempt to "overplay" the moral aspect of it. You seem to be arguing (correct me if I'm wrong) that mental illness isn't the distal cause of suicide; or that there's some process between the two that can change the outcome (and it seems to me that you're arguing that is a sense of morality).
I have as much evidence to support my claims as you do (i.e., 0), but I don't think people who are mentally ill enough to be considering suicide would stop and think "is this the moral thing to do?" before carrying out the act.
To your question about rates of belief on the moral nature of suicide, I think it's possible. I also don't think it matters at all. People who have planned and attempted suicide are far more likely to be compassionate and empathetic to others in that mental space.
Another thing worth pointing out is that morality is far from a uniform idea. There is no universal morality. I think there are some basic tenets of any human morality, which is why irrespective of one's upbringing, humans tend to be have the same way (and seek the same things in life [e.g. life, love, prosperity, meaning, companionship, friendship, etc.]), but two people can have different views on, say, suicide, with each coming from a "sound" moral perspective.