Not sure if I follow your reasoning but here are my thoughts.
You could cut each layer out then glue then back in using small pieces of wood as spacers. If using 6mm thickness wood, each spacer would be between 2 - 4 mm thick.
You could cut everything by tilting the saw table so the bottom layers stands bashful, the middle layer is cut normal and the front layer is cut proud.
Hope this makes sense to you, if not feel free to respond off line
Dock