FYI: The effect you are seeing is similar to what I have been getting trying to cut Mother of Pearl. Both the eggshell and Mother of Pearl are primarily calcium carbonate.
To report a failure: I can get through the MOP with high power or even many low power passes but I’ve determined that cutting thick MOP (0.06") is pretty much impossible to get a clean usable cut. It shatters, burns or turns into a cement that clogs the cut. No power level, speed or number of passes has given anything worthy of using for an inlay. That’s not to say that much thinner material or Mother of Pearl laminates might not work. But not the thickness that is typically used on fretboards. Will try the very thin laminates after I can get some in. I suspect those will work but they are mostly just decorative vs. decorative and durable.