First of all, I am so sorry for all of your pain and struggle. I have a lot of compassion for your situation.

Switching medication in and of itself can cause much emotional instability.

You seem to have a great deal of insight into your situation, and I feel a lot of success of any type of treatment is the client's "buy in." Unfortunately, therapists and psychiatrists have to work according to a predetermined "standard of care" that has different levels and if a person is suicidal, it's pretty much accepted that person needs to be on medication. And our current medical system is pretty jittery about lawsuits and such and that doesn't allow for much in the way of looking at creative solutions for individual situations. Your therapist may very well understand and possibly agree with your decision not to be medicated but can't say that because of ethical reasons.

I'm not sure what your diagnosis is, but have you looked into DBT? It was designed for Borderline Personality Disorder, but many, many people utilize it for other things. Mainly, it does seem to cut down on suicidal behavior. One advantage it has is the use of groups which would be another source of support. Since you seem concerned about your therapist's single role as support, maybe this would be a good thing. I have not done this myself, but I watched a talk by the creator of DBT on suicidal behavior and was impressed about how this particular therapy cut down on attempts WITHOUT the use of medication. I think I have the link to the Internet video you could watch. Again, Borderline Personality Disorder has an unfortunate and undeserved stigma, especially considering its causes are from horrible childhood trauma, but this treatment addresses any kind of distress and in particular suicidal issues from any reason or disorder.

Good luck to you.