Hopeworks, I am sorry, that I don't know the phrase, either---even though I am familiar with the Concept. I think that the Concept is what is important, and,it sounds like you have gotten that down. You have my complete empathy with your position.
I have worked with people at various levels of damaged personhood, most of my life---and, I have faced similar. It sounds like you hare/are doing as much as you are capable of in this situation.
I understand the desire to "reach" them and alleviate their suffering. This means that you are a caring and compassionate person, to feel this way.
I think that we offer them what we, realistically, can---we do what is possible---then we have no choice but to turn the rest of it over to God (The Universe).
As for your "self talk"----I think that the Serenity Prayer is as good as anything.