This is terrific! It manages to convey a huge amount non-verbally and lets the puzzle emerge organically out of what the player observes, reminiscent of the excellent puzzle design in the Witness.
A couple of observations without spoilers:
1) The use of music tipped me off to something in a way that came from outside the game rather than within it. Maybe it's too purist, but I wonder if there's a way to have something diegetic (ie contained within the sensory reality of the game world) perform the same function?
2) There's a solution that doesn't require interacting with one of the rooms/fully exploring/gathering all items. (I'm not sure if this affected the outcome)