I went ahead and bought a dedicated vessel for the task and used it for my second go at a pair of steaks. I remembered to pat the steaks dry before searing them, and really cranked the heat on the cast iron skillet. My infrared thermometer was showing it at 600 degrees when I flopped them in. I could have gone higher but I was afraid I would burn the seasoning off.
They came out some better than my first go, there is almost no grey along the edges of the cut and the sear is better developed.