Do you always have to run the meeting? What if you didn’t? What if two members of the team did it? One of my clients paired two warring members with a high-profile meeting where they were forced to cooperate. After a few of those meetings they became fast friends!
You really don’t have to do what THEY can do. If you're a leader, try this! Show up at the beginning of a team meeting with an inquiry about what everyone wants to accomplish, give some very brief perspective remarks, then leave! Returns for the final 15 minutes with innocent curiosity and lots of encouragement. Let me know how it goes!