Personally, I like what you are doing without the use of dye. I think that letting the various hues of the different species of wood makes these pieces unique, challenging, and more in spirit of the artist than using dyes. One of the problems I had with Neoplasticism is the quantity of artists that would use this as kind of cheating way to try to make a quick piece so that they can make a quick buck. Not a personal criticism of your work, I think it is a brilliant idea for boxes.
But, in my humble opinion, I think these would be more exceptional if you challenged yourself to mimic the style with the natural wood colors. There are times when you won't be able to find the exact color to match, but the efforts would still add your own unique vision to the concept. And the beauty of it all is that wood colors change over time, depending on exposure to light. So you would also have a box in which the colors would undergo change over time. So the piece would never stay the same. Which is kind of cool in itself.
My two cents
David