I wonder if attempts to prevent charring of such a design could be what led to pottery. One can imagine smearing mud or clay on the underside of bark or animal hide pots to increase their longevity. Long enough exposure to high heat and ?

yeah probably

I also wonder if people tried to layer various material to cook them at different speed, a form of ad-hoc thermal control

Yep. Lots of examples on YouTube: https://www.youtube.com/watch?v=xV2gsWHhDhY

Very impressive