First, thx a lot to do something to this issue. I saw that you use the example in Korea. The result comes out that after they did the make-over with the signs, pictures and the phone booth, it attracts more people to choose to end their lives there. ( 4 times more than the previous year) It is hard to find the right things to say, some signs will make them more angry. So it may not a good example for the UX/UI for this case.
And for the design: I think it is hard to let people to click on the first thing. If they think you are, as a search engine, just try to get them not focused on the question they ask, they will close the page and try another place to look for. So why not try to trick them? Make every category looks like the perfect webpage. I think it will make people to relax and read the stories. They’ll read the page, the story which with the perfect title. If they read it, then they’ll feel better, that they are not alone, someone out there also got the same issue and they made it. For example John lost his hope for education. Then he will read such article: I failed to get through my University and I am so done with that. (I know, it sounds angry and sad and more suicidal, but that’s only to make them click the link. And in the webpage has to be a perfect story, so it’ll do some help.) This ist only my own opinion, perhaps you already thought about that, too.
Thx again to do something with this topic, it is a real problem for the modern society.