I think in this situation, less is more. I would bring the 5DMIII, the 70-200, and either the 24-70 or the 50mm. If I were doing this just for the Company, I wouldn't want to be bogged down with all this equipment, changing lenses, toting around a big camera bag, etc. You want to have fun at this event too, I'm guessing. Being outdoors, the 70-200 I think is plenty to catch the action up close. The wide angle or the 50mm prime would be good enough to capture the scenery surrounding the events.
I don't think you need a backup body. If your camera bugs out, remember you aren't getting paid. Same thing could happen with someone who volunteers with a point and shoot.
Less is more.
I agree, the 70-200 and 24-70 would be exactly what I would bring (I have them both and use both for high school sports, in fact that is what I use for indoor sports with a 5DIII and a 1DX). Along with a flash for dark situations, you should be good to go. If you can, you could add another 5DIII or 7D. I would prefer the 5DIII just for consistency and familiarity. It doesn't sound like you are going to be restricted to the sidelines or behind barricades like you would at competitive sporting events so you won't need the longer reach of the 7D and again not having to learn a new set-up would more than offset the crop factor IMO.