Personally I would not do a black on the walls, it will make the stove blend in with background. I love how the stove jumps out at you, the way you have it now.
I was just wondering if that was a reflective material. I used to have a barrel wood stove in my garage. It was close to the wall so I hung sheets of aluminum foil behind it. When I held my hand between the stove and the wall it took about 30 seconds for the radiant heat to feel like it was starting to burn. If I slipped my hand under the foil the wall would still be cold. Just shows how reflective a thin sheet of a aluminum can be. Just as effective as a mirror with light waves.