We will need a good mass and insulation in the ceiling to catch and radiate the heat downward.
Actually, we don't need that much mass
I don't know anyone with a drago, so I can't say for certain how long it takes to heat a cold, fresh from the factory (or long vacation) oven, but Jeff has pointed out that it most likely takes a very long time, which I'm not disagreeing with. A contributing factor to that time is the thermal mass in the dome. As you scale it down, drop the thermal mass, lower the ceiling and go with a much higher BTU to mass ratio, the time shrinks considerably.
I'm not completely ruling out insulation here, but, as I told Bob yesterday, this is basically LBE thermodynamics. In your average LBE, with the lid on, the proper size vent and a typically high BTU burner, the air foil/director stays plenty hot, regardless of the lack of insulation above it.
Now, I'm not necessarily backing the metal plate ceiling idea. That could require insulation. I'm thinking some mass- 3/4" or thicker cordierite will, with enough BTUs glow cherry red and shower the hearth with all of it's radiative goodness.