My first oven was made of cob dome that I formed over a pile sand covered eith plastic bag. Around 10 cm thick, no insulation and non insulated floor that was sucking all heat. The opening for fuel was also the chimney. It was quite miserable and very difficult to bake anything.
My second one was a flattened batch rocket firebox - fi 200 mm equivalent, made of dry stacked red bricks. No insulation, but we managed to bake some inferior breads and sometimes good pizza.
Based on that firebox I built a real dual chamber oven, with firebricks, a lot of insulation and real cast iron doors. It burns super clean. I love it, but would make one improvement - complete insulation between the firebox and upper chamber, so after the burn, the upper bricks would not suck firebox heat. We bake a lot of breads, rolls, pizzas, make stews and smoke. Pleasure to use. It keeps heat for two days, so it can be quickly reheated to baking temperature.
You said that you are counting on having the oven floor to be heated by firebox ceiling. My measurments consider it to be inefficient. When the brick outside is 70 C - hot to touch, the interior is 400 C, so to heat the floor sufficiently, the ceiling will have to be heated to red hot temperatures and it will quickly compromise rather thermally delicate cob. That's why I always recommend traditional approach, used in all bakery and pizza ovens: firebox is the oven. This way you will always develop sufficient temperature without wasting fuel and the oven walls. With insulation all around and chimney damper it will always work. Around 40% of wood burning energy is emitted through radiation from flame and coals. When we add conduction of coals and convection heating of the firebox it will turn out that at least half of energy is in the firebox. The rest is heating the fues, other chambers, chimney and air.
If I wanted to build an oven as separate chamber I would build the firebox from insulating firebricks to direct as much heat as possible to the separate oven. I would also make the ceiling from metal (would need to be some quality heat resistant alloy to survive). I would also pad the door with insulating material to prevent the losses due to radiaton towards the door.