As feared, the components do not easily fit into this box. With the vast bulk of the components being “tiles in a bag”, this should be the epitome of “throw everything back into the box and pop the lid on”, but my first attempts weren’t even close to successful.
I can confirm the approach shown in How to Re-box Standard Edition (neatly)? | Ra works. Against all intuition, you need to leave the draw-string bag fully open, but it works out because the bag fills the length of the box, so the tiles won’t actually spill. You then have to massage the bag to distribute the tiles evenly enough to get the lid on flat, but that turns out to be easy. The only issue then is being careful taking the bag out again (tilting the box so the open end of the bag is facing up) – and of course knowing the re-boxing trick in the first place.