Mixing cheese into bread

Yesterday I made the Soft Cheese Bread from Reinhart's Artisan Breads Every Day. He instructs to mix the onions/chives into the dough but to layer the cheese on the flattened dough just before shaping. In my case, that created a cavern in the bread where the spiral is. I'm not necessarily bothered but there has to be a better way.

Is there any reason NOT to simply mix the shredded cheese into the dough just like he has you do with the onions? Yes, this would mean you'd have cheese bits on the outside/crust, but wouldn't it also help with the enormous hole?