I normally carry a short tree strap that I use to hang my pack off of one of the trees, and throw a pack cover over it. anything inside the pack I will need goes on either the ridgeline or suspension. I tend to compartmentalize stuff into rolltop drybags, so it is easy to clip right on. As for changing, I drop the tarp sides pretty close to the hammock if they aren't already, climb in and change while laying in it. I also have a Clark NA with the weathershield that I will use if I know I am completely going to lack privacy. It may look funny with me bouncing around in it, but no one can see a thing!
As a Scoutmaster, you may want to look at a bigger tarp and tarp doors, and spend some time on site selection to make sure you are positioned correctly and out of any thoroughfares!