First... Beautiful piece!
My attempt to answer your question. Ever cut you make you lose a small amount of wood due to the thickness of the blade. It sounds like your work was cut from one piece of wood as segmentation. When you piece them all together you can lose a lot from the kerf. In intarsia, the pieces are mostly cut individually to the exact size or very slightly larger, then sanded to fit perfectly. My experience with intarsia is to cut a few pieces the fit them together. Then cut an adjacent piece and sand to fit. Then keep repeating. In my little brain it makes sense, I hope it makes sense to you.