The lack of the headmaster won't make any difference to the board's objectives.
They want to see rounded, intelligent people who can think a problem through, explain their thinking, come to a conclusion/plan, and show that they can lead others to execute the plan.
The group discussion phase is hard - either if the group is full of bright guys who all want to get their ideas across, or if the others are numpties who haven't got their head round the problem(s). My advise would be to stay on the cool side for the first 25% of the time allocated until you've worked out where each of the others is coming from. Then up your involvement to get your ideas into the mix.
You will also have to have the answers to the awkward questions, and show that you've done your homework on the Service.