What a great project. You already have draft out the chimney. You just need to figure out how to build up fire brick for a cooking surface. I can share a photo of one of the nicest brick ovens I've seen. The split wood burning is directly below the exhaust vent. and the fire brick dome and floor absorb the heat. They start a fire in the morning and measure cooking temp with an IR thermometer. Usually the floor is 500° to 700°. A pizza takes less than 2 minutes, and a T-bone takes maybe 3 minutes. The oven is deeper than it appears in the picture. And because it drafts so well, no smoke comes out the front. They do have a half round steel plate they can set in front when the oven is not in use.