All great ideas. 

One of my thoughts would be to have a large fire with three 
sides stone or the like.
Have a piece of roofing metal on top of rows of bricks. 
Making long narrow compartments or revetments.
Of course this requires metal (not so abo). Now with a continuous
large amount of coals on top of the roofing metal you could slip
 different cherts into different compartments
and rake coals to heat and rake them away to cool.
The preforms could be in baking pans or cookie sheets covered 
in the amount of sand  thought to be required. From my experience 
the crucial temps are the high ones 300-500 degrees.
Just a thought. Using smaller fire wood would help keep things more stable.
This way you could take some out and put more in. like a Pizza oven. 

Wouldn't the ancients laugh. 

Zuma