This is an interesting post, but I'm perceiving something of a deficit in allowance for individual variation.
Put more directly, three relevant items may differ according to the individual in question. First, target stress. Second, which sorts of inputs increase and decrease current stress level. Third, reaction to increased and decreased stress levels.
I mention primarily because the items noted as calming would not be calming to me, and to a lesser extent because I have the impression my usual target stress level is significantly above usual (the two are likely related: lack of stimulus will increase my feelings of unease rather than decrease them).
That aside, some good points were made.
I don't feel it would be appropriate to put too much of my own opinion into this discussion (because I happen to be very strongly pro-choice on the matter, having made several attempts including a fair number of Intensive Care Unit hospitalisations myself), but I think it would be appropriate to clear up a particular common misconception which it seems you are currently accepting. Namely, "Suicidal ideation can usually be treated in clinical settings."
In fact, the literature to date has suggested that modern clinical treatment markedly increases the risk of subsequent attempts. Specifically,
Having been hospitalised for attempts myself and exposed far too often to the modern clinical system, combined with the best evidence available, I am of the opinion that modern treatment, if anything, increases both the level of suffering in the general population, and the risk of suicide itself.
If I had to propose an explanation for this phenomenon, I would say it's likely related to the "...wealth of academic and anecdotal evidence" which "documents how suicides traumatise witnesses (e.g. train drivers, police, paramedics, family and friends)." That is, said trauma is indicative of a self-focused response termed in the psychological profession as "personal distress," which has been shown repeatedly to sharply reduce empathy and lead to poor treatment of the perceived source of the trauma. The perceived source of the trauma is, of course, the person who is suicidal; the result is quickly and continuously escalating negative outcomes for everyone involved.