I walk between the two groups as they discuss. I have found that the negotiators are so intent on negotiating that they do not listen to the other discussion. If you have a large auditorium, use the four corners and put opposing teams in opposite corners so you will have two blue teams in one corner and the corresponding red teams in the other. And vice versa for the other corners. I have had teams within 10 feet of each other with no problem.
Discussions tend to cause groups to filter each other out.
The drawback, of course, is that you are not able to observe each team fully. Appointing an observer helps during deprocessing when using this alternative. If you have the luxury, suggest establishing a round robin between this exercise and another one or two. I have found you can reduce the number of rounds without losing too much so can reduce the time of the exercise to about 20-30 minutes. I am leading a day on team work on Martin Luther King Day for about 120 employees of a small public utility.