Acknowledging this divide, I used more “push” techniques than I typically would to try and bridge the two divided groups: actively giving feedback and general advice in some situations. That said, I still spent most of my time using “pull” tactics: paraphrasing what other people said and then posing a question to pull in other perspectives on ideas, etc.
I see your awareness of the group dynamics in the room as reflective of your training as a facilitator. I will be actively following your work on here to better learn and understand how to do large-group facilitation and coaching - thanks for sharing your knowledge with us!