Can I throw an alternate out there? Unless you can control the lighting in the competition, (my HS theatre competitions were given nothing but classroom florescent lighting, but it's been a long time since I was in HS) this projector setup is going to get pretty complicated pretty quickly. When I use rear projection on stage, I'll stack two projectors on top of each other in order to get a reasonable brightness. And seeing that you're not going to be able to borrow a projector from the school, your project is going to be pricey.

Instead, maybe you could borrow a flatscreen TV, either from a family member or one of the students. Then mount it on something like this. This way, you only have one thing on wheels to control. You can set the screen as far back in the space as you'd like, and you don't have to worry about the issues with projectors.

It might not be as big as you'd like. (Seeing that your currently looking at an 6 foot high screen!) But it would definitely help suggest the setting without spending a crazy amount of dough. If you can borrow the screens, then you could get 3 wheeled VESPA mounts for the same price you were willing to spend on the whole project.