The web is full of specific tips and tricks for doing deep conversations. Used in the right situation, they all work. Used in the wrong situation, none of them do.
More important than the particular set of rules or behaviours you set for your conversations is to talk explicitly about what those rules should be. Make time upfront to talk together about what could make this conversation different from other conversations for you. Choose qualities to focus on. Decide together how you are going to express them with your behaviour.
More effective than struggling to keep in your head the best tactics and techniques is simply to notice that your conversation has those two levels: form and content.
A campfire is an ancient and universal site for deep connection and conversation. Think about your conversation space in campfire terms. A campfire isn't something you can "fire and forget"; it needs to be tended.
We all bring our own meeting habits to any gathering, and we won't flip into a new mode just because we talked about it once. We will forget where we are. We will slip into more familiar modes of interaction. It's like learning to meditate. When you notice your conversation is wandering, that's okay. Recognize it, shift the conversation to talk explicitly about form again, then get back to the content.
As a group, take the time to tend your fire.