I don't wash mine or bake them. I set them on the counter and let them dry not cradling so they don't get moldy if I don't take em out right away. I just crush them a little and toss them out or pout them into their OS container. Yes, they always eat the egg shells first... but it may not be enough calcium by itself long term. Having the OS available on the side as you do is great.
As stated, keep your treats below 10% and be aware that many things touted for protein content such as BOSS, meal worms, and scrambled eggs are fairly high in fat.