FWIW about "busybodies", I had a friend get the fed sicced on him when a housecleaner or some other service oriented person noticed that he had lots of radios in his house (big units on racks, not clock radios!), post 9/11. The ATF ripped apart his gun collection looking for infractions. Just pays to keep what you got away from curious, ignorant eyes. A sheet hanging in the right spot (or a closed door) could have saved him from LOTS of legal trouble.
Oh, as for my moving story, when I PCS'd from Hawaii, I packed everything into my Homak locker, secured it, and handed the movers the case. IIRC, they wanted a list of serial numbers, so I had to unpack everyhting right there. So it may behoove you to record this info BEFORE packing. Whether they have the "right" to such information is between you and the movers, I guess. Who is to say what is in a locked chest labled "Exercise equipment"? Thats how I'm moving my ammo next time.