So it turns out these are both breaks, and the lantern was supposed to be all glued together. No biggie, everything fits together perfectly with the peg/hole system SS used, even without glue (but I will glue it). The $45 credit SS gave me is icing on the cake, as far as I'm concerned.
Some shots of the base. The lantern itself comes off the base, but I have no idea how to get it through and out of the rest of the base. The top "cone" of the lantern is also a separate piece.