Well, they're definitely not a population with a 41% suicide rate, and probably not a population with a 41% suicide attempt rate. The study where that statistic comes from uses a sample of convenience.

The tl;dr is we don't know, so we shouldn't frame our decisions and policies as if we do know.

Specifically in this question: is a surgical/endocrinological approach or a mental health approach more likely to result in positive outcomes?

I don't think this is the place to debate standards of care for trans people. Here's a review of some literature, if you're interested: http://www.sebastianmitchellbarr.com/blog/2015/10/8/why-are-...