The door is looking good.
I made a replacement brick with a plaster of paris and silica flour ratio of 1:1 with 3:1 water sodium silicate ratio. The now expected clumping, curdling, showed up. I worked through that and added perlite in some unknown quantity. By then I had lost control and just wanted to finish it. The brick looked good the next morning but a day later it had self destructed. This block was only exposed to ambient temperatures.
EDIT: it may also be a case of either the silica flour or the perlite sucking water away from the plaster causing it to not set or fail after setting.
I took one of the broken bricks from the side of the oven and encased it in satanite. The form is covered with packing tape.
To be continued...