I get all of your points, but if I'm completely honest, nobody makes good stories about suicide, not what I have read anyway (and I have read a decent amount of comics). JtHM is probably the closest and that one has all these horror aspects that, while I like those, take a bit away from the suicidal aspects. Most comics I have read just have other characters yell at them for attempting to kill themselves which really offends me. I think those comics are really harmful to real people who deal with this shit.
So I just decided to go for it and make my own comic about my personal experiences. It does critique the healthcare system quite a bit, but that's because the clinical understanding of mental health is really really shit. Seriously, I have done a lot of research and the difference between mental health science and what they actually use is disgusting. Not to mention how the very early psychologists were never considered in mental health (even though we are now finding out that their more humanitarian ideas were completely right)
Anyway. I released my first page a few days ago and I got a person, saying that they are a retired mental health nurse, complementing and thanking me. I know this is just one person, but I think it kinda proves we shouldn't be too scared showing these very real things.
If you want to not have clients connect this comic to you, you should seriously consider making it under a pseudo name instead. It's the internet, nobody is going to judge you for doing that. Lot's of minorities (gender, sexual, religious, political, mental health, physical health) already do that so why not you?
And about being scared of accidentally encouraging suicide. And this is just me personally. I have read so many people talking about their attempts and why they did it, and all I ever felt was a sort of comfort that I'm not the only person who feels like this. Being suicidal is a very lonely thing because I have never met a mental health professional who even came close to understanding me and my best friend (as much as I love him, and how much he tries to help me) doesn't understand this about me either. And because of this loneliness if feels so important to share our experiences.
The only discussion about suicide that has ever made me feel more suicidal are when people try to tell suicidal people that our life does get better and that we should think more about our friends and family. This hurts so fucking much, especially when it comes from people who have recovered from the mental health problems. This has legitimately made me try to die a few times.
All in all, I think you should just go for it, even if you do it under a different name. I'm really sorry for how long this post became. I just care a lot about suicide awareness.
Here's my comic in question: