I believe this forum is somewhat old, but I read through some of your ideas and loved them! Personally, I like to think Molly gave Sherlock some kind of special access keycard (or something) to the morgue. It's something that is valuable because it risks a lot on her end and would mean a great deal to him, helping him to bypass the system even more than he already does. It would save time and energy and keep him from interacting with (live) humans. The box is thick because Molly (being Molly) would have been careful to set but the keycard in some kind of slot or special stand. I mean, look at how carefully she wrapped it!