I haven't experienced too much smoke yet, and I use 3 oz. of wood for just about anything I smoke. I have a the baby SI, so maybe that's why? But yes, maybe if you wrap it up and give it some time in the fridge, some of the smoke might penetrate deeper into the loaf.
I'm curious about the cheese. . .how do you incorporate it into/onto the loaf? Where exactly does it go?