The lap joints are possible as the stamp box demonstrates. With the 1/8" ply it doesn’t take too long to engrave the rabbet/rebate. Does take some understanding of designing the mating surface as mirrors but that is basic woodworking.
This post demonstrates the process. I haven’t tried it yet, but it would be a good challenge, especially in hardwood. The inner ply of the 1/8" might not be suitably dense enough in relation to the surface plies to engrave the gradient equally over the angle. There have been tons of long discussions about this.
The biggest obstacle for me is designing the gradients of the angled engrave. That would have to be a bitmap at the moment to get the engrave gradient place over a vector cut file. Although @dan_berry demonstrated gradient meshes for me and Inkscape does them well, at the moment it just would take long for me to design it. If someone wants to do a test file for me, I can try it.
It certainly would be a nifty trick to pull off.