Hi!
Here you go, how I do inlays. With this method, it’s the stroke width that’s key. That you will have to determine yourself by testing with the actual materials you will be using.
That’s a complex job. I’m thinking I would work from the center out. Since the laser leaves a beveled edge I would invert one of the two so that they fit better at the joint you point out.
Now the two nested pieces each have a different angle on the outside edge of the circle they created, so I would expand the diameter of the whole circle enough so that I could trim the ring with a cut to have the same slope around the periphery and work outward to the next element, the blue ring. Keep in mind the cut slope of the previous edge so you know how to flip the next one.
Good luck with that!