Ikea confirms that the clock is made of white polypropylene, transparent polystyrene (laserable according to a google search, but settings tbd) and ABS hands. A quick check of the laser's effect on the polypro shows it is a good to go (5/40/5000). Since I am etching and cutting the actual 3-D clock, I can't do a practice on cardboard. I double-checked my geometries, used the calipers twice, pinned my pieces in place and flipped the laser on.
Next time: Zero the calipers.
Thank you, Anna Ly and Michael Duong for donating the remains of your clocks to me!