It's great that you've recognized the mental health issues and that you've realized an intervention is needed. Emergency mental health outreach in the shelters is one aspect of being able to do that.
I will go back, though, to my original comments and say that it may not be the long-term answer. Housing First we know is an approach that will end homelessness for those experiencing mental illness. Reducing the reliance on shelters for those people and providing mental health supports come with the Housing First approach.