Probably what happened was that Honest-But-Chatty Employee 1 saw your big wad of cash out in plain view, took nothing, but mentioned it to Quick-Fingered Employee 2, who later was in your room and, ultimately, searched your backpack. This was the work of an old hand: He/She only took a small part of your stash, betting you wouldn't notice until you were long gone (a novice would have taken the whole thing and see you raise the alarm immediately).
I've been in a similar situation. In the end, I chalked it up to "my bad," let it sting a bit, moved on. It's a $200 lesson. Trust me, you'll never neglect to use the safe again.
That said, the hotel clearly has a thief on its hands. They should be told what happened and perhaps a manager who cares enough will get enough of these letters and start piecing it together. Don't count on it, and nope, it won't be of much benefit to you, but that's probably the best you can do here.