I was wondering how one could test if "objective" time exists in a measurable fashion, and had an idea for measuring time that I think is fairly novel: Clockwork origami!
Using pencils as axles and folded stars as gears, given near infinite time, I could (optimistically) fashion a small timer that should maintain its state between intervals while it's sitting inside the desk, assuming objects don't get shifted around "in between" iterations. The real difficulty, I imagine, is figuring out a power source. Harness gravity using paper twine wrapped around a pencil, with a weight on the end? Desk is probably too shallow for that, but then again it can fit people inside it... Wooden spring made from thin slivers of pencil? How I'd slice a pencil using just my fingers and my teeth, I don't know... Maybe an "hourglass" consisting of a paper sieve and graphite dust?
The limitations of the room have really made me think in weird directions. Once again, great job.