Hi, you seem to me to be over-complicating a simple situation. I don't mean to talk down to you, but it is just a fireplace. If I were doing this project, and I would love to have a wood fired pizza oven, I would make the flue and the opening around the same area.
I would make the opening as small as is practical, maybe 14" for a 12" pizza plate. In the flue I would have a damper that can be regulated with a screw device for precise adjustments that stay put. It may not be a 2000 year old approach, but my truck has air conditioning in it so I see nothing wrong with going along with modern technology.
Am I missing something?
Make mine a meat-lovers with anchovies please.