Today I've set up two more moisture penetration tests. One is the same box with the lid sealed using tape. The other is a bit more interesting, and I have great hopes for it.
I've thought on what other container can I obtain for filament storage. I thought of using sauce pots.. but then I decided to try to moisture proof my boxes with alimunium foil tape. Aluminium is absolutely moisture impermeable - even its few-nanometer-thick oxide layer is, which protects extremely reactive aluminium from oxidation.
So I taped most of the surface of the box and the lid. It isn't very important to cover all area with no gaps - for my purposes, based on previous measurement, a 10x improvement is going to be good enough.
Now, all I do is wait. In about half a month, I expect some preliminary results.
UPDATE. Five days since start, none of two containers had gathered measurable amount of water ( < 1 g)
UPDATE2: 3 more days. The one taped with al foil has gained 1 g. The other one hasn't changed. I'm about to draw a conclusion that permeability of plastic of the box is negligible.