Soooo, almost 5 months later, I finally gave it a shot. First time around, I looked at the moon before even finding the first radio...stared way too long before realizing nothing was happening.
After the broadcast, just for gits and shiggles, I immediately went out and looked at the moon.
As for the actual objective, it's not inherently clear that you're supposed to turn the radios off, and at times the compass doesn't leave one you've already turned off.
However, altogether, for as short as the experience was it was amazingly atmospheric.