Thank you this is a very thoughtful post .
I think you start by really trying to understand the other person’s perspective.
For example, with my husband, he would accuse me of “talking in riddles”. I thought about this and realized that he had a point: in trying to avoid saying things that would cause him distress, I was being evasive. Ultimately, when he kept backing me into a corner, I did tell him what I thought. He disagreed (of course) and was quite upset initially, but ultimately it allowed us to “agree to disagree” and started the process of his feeling more trusting again towards me.
Your situation sounds much more volatile than mine and incredibly challenging. Perhaps you could start by reflecting the distress that must underlie his accusations (how awful you’d feel if the people who should be there to help are actually doing whatever it is he believes you are doing)?
Your suggestion is a good example of using the LEAP strategy!