Curious mold growth in a sealled BBQ, how does one avoid it?
Mold is growing because there's something for it to consume, the only way to prevent it from happening is to clean your grill more effectively, or carbonize it before the fire goes out. No grill is air-tight, so even though it gets a good heat blast (not enough to sterilize it as you may think), spores will get in from outside. Remember, hot air is less dense, so as the BBQ cools it will draw air in, hence the spores. Once there they thrive in the sheltered and often damp conditions in a closed-up barbecue. 

I think where you may be going wrong is that you close the valves after cooking. That cuts off the air and kills the fire. I leave all my valves open to keep it as hot as possible after I'm done cooking, and it does a better job of charring all the leftovers.