Re the security issue on guns stored flat in cases, I have recently begun improving a couple of closets to add a little security. In an upstairs office closet, I replaced the original hollow core doors with thicker solid core doors that match the appearance of the originals. Added exterior door lock sets and single deadbolts that match the finish of the interior trim, and replaced the jambs and hinges. New hinges are non-removeable pin type. A crowbar or saw will still gain entry to the closet, but more casual visitors will never see the inside.
For the safes in the garage, I am in the process of building a closet to enclose the safes. Closet will have case storage above the safes, and the interior walls will be lined with chain-link fence material to deter intruders. Steel fire doors will be hung in steel jambs with NRP hinges and locksets/deadbolts. The cost of the closet materials is about the same as another decent safe, and the closet completely hides the safes from view.
