Learning to work several groups together on the same projects is
certainly relevant traning for the industry. It is a big challenge
for most companies. Good technical skills are important but good
projects management is also a key issue on large projects.
I think using Scrum is a great idea.
1) How would you devide the responsibility between the teams. (this
is where project mangement meets architectural or domain model
2) Will you be allowed to train the superviser as Product Oweners
(this is a situation we are confronted with every time we introduce
scrum to a customer)
3) If you arrange it so that everybody works focused on the project
at the same time say monday and tuesday to minimize task switching