Having got this out and looked at it again, I think Sue may be right that the top and bottom may in fact be a marriage! The wood of the base is different, and much coarser grained - less well finished! I think it was possibly made to replace a lost or broken base, as it is clearly 'in the style of' the pagoda-type lid.
I've looked at (and smelled) the inside again, and I think that whatever it was originally made for, it has possibly never been used. Nutmeg is indeed a possibility, I'd have thought, but if it had been used I would expect some trace to linger, as the lid is a good tight seal.