smoke is often a strong flavor--generally. Mozzarella and eggs are milder flavors. I think you need something to stand up to the smoke more. Maybe caramelized onions, maybe dill/chives. Capers could do it too with some sour/salt impact. And for a stronger cheese, something is a swiss/emmentaler/goutaler family would be more to my taste in this application, used with a light hand.