"But I am looking specifically for how to enter into interactions where the outer critic is clearly coming up for the other person. Any advice/experience is greatly appreciated. "

I'm sorry but I don't understand - duh! - do you mean by "outer critic" that you are criticising others, or that you externalise your inner critic, or that the other person has issues? Everyone else here seems to get it, but I'm not familiar with this term.

Please could you explain?