Do you have an infrared surface gauge? 350-375 is the highest I'd go. Beyond that the seasoning risks getting ruined. Soon as cooking is done either cut off heat to the griddle via your cookers internals or remove the griddle from the heat. Don't let it stay in/on the heat.
Got one of those -
Thanks for tip on removing from heat - I can just pull the other grate and slide over away from the coals