I know nothing about the boxes, nor which wood movement ruless they violate successfully. If you design your box with a larger gap to accommodate wood movement in the door, then you are not violating a wood movement rule, you are designing to accommodate for wood movement.
The cutting boards have a decorative strip whose grain runs counter to the body of the cutting board. Based on my own experience with similar designs, I predict that over a period of years:
* Notches will appear at the top and bottom of the strips, as they contract more than the body of the board.
* Gaps may appear between the strips and the long contrasting thin strips adjacent to them. There will be stress in the glue between them, as the glue fights the differing contraction rates of the main strips and the thin inlays.
* Cracks may appear once the glue loses the fight.
I know this because I have see it happen in projects that I have built. Be patient. It may not happen for a decade or more, but eventually it will come.
There is one advantage to your design: The main body of the cutting board is unconstrained on either side of the strip. If you had built it with two separate strips instead of a single strip, the problem would have been far worse.