Blending Solids/surface advice

I have two aspects of a model that I need to blend/transition smoothly. If anyone could advise on this I’d be very grateful. Model is attached. I have a bezel that needs to blend into the texture of the surface of a box. (1.1 MB)

I would cut out the space for the bezel, and then build the bezel so that it blends as required. Sweep2 would be one of the commands I would use.