This is similar to the challenge that we did on the deep dive for my AOW course, but in reverse. In teams, we inflated a balloon on the surface, took it down to 85 feet (happened to be the depth), measured the diameter with a string that had knots at 3 inch intervals, and multiplied the knots by 3 to convert the diameter to inches. The purpose, I think, was to see if we could work as a team a and solve a problem while narced.
The thing that made it tricky was that as well as shrinking as we descended, the balloon also stretched up toward the surface, so the neck was long and thin, and the top was more of a sphere. I wonder if holding the balloon in a mesh bag, or putting your hand on top, would keep the shape similar regardless of depth?