I recently noted that Mike Rowe, host of Discovery Channel's Dirty Jobs is an Eagle Scout. I know (having been at the jamboree) that there are a lot of dirty jobs available and Mike should easily be able to do a whole show about the jamboree.
I agree that cleaning out latrines would not be a good one. But working the grinder, delivering ice in the middle of the night, and working food prep would be good places to start. The chance to be a part of either the opening or closing arena shows would be a draw as well. If nothing else, get him to do the National Anthem (he used to sing with the Baltimore opera).
I agree that latrine cleaning shouldn't be a bit part of the show. Having also worked at the Jamboree, there are so many different parts of putting on that event that are dirty. It may also be a good way for us to work with the military to show what they do to help support us, and what we do to help support them, to show the positive aspects of our relationship.