As requested, more pics of the box of bits. The sides and lid are all 3/8" thick and outside dimensions are 10 1/2" long, 3 15/16" deep and 3 3/4" high. For more dimensions there's a not-great but dimensionally pretty good Sketch-Up file here.
The top tray doesn't seem to be full depth but has an extra 1/8" or so thick bottom. Also not full length grooves for the smallest bits - which gave me all sorts of headaches with SU...
The second tray seems to go "right through" with no additional bottom. Note the original wax paper wrappings on two of the bits - gloat, gloat, gloat... ;)
The bottom tray seems to provide the bottom of the box too - and another bit of original wrapping.
Finger/comb/box joints at the corners. I'm assuming the whole thing was made as one and then cut into three tiers and the top added afterwards. There's also a slip inserted across each end of the lid.
Interesting hinge, no?
Horribly tempted to "hang spring cleaning" and have a go at making one. Only problem is I don't see much cause for boring holes in such a project, and I have an urgent need to bore holes. Lots of holes. In corners, where a ratchet that whirrs like a Swiss watch would really show its stuff...