The way you are doing it seems overcomplicated... Just put the firepit on top of the wood pile. In this game this works.
SSSSSSS
SSSSFXP
SWWWWSP
SWWWWSS
SWWWWSS
SSSSSSS
S - stone block around the charcoal pit, W - wood, F - firepit, X - firepit access, dirt block to seal the lit charcoal pit, P - player, bottom and top half.
Fill in the charcoal pit with wood. Put a firepit on top of the wood pile. Light up the firepit and you have 30 seconds to put a single block to seal the charcoal pit.