On occasion I get water build up in my airbox as well, and the cause is still somewhat of a mystery to me even after 4 years.
It seems to only happen when I use wetter wood and the weather is warm. I'm thinking long idling lets moisture build up in the airbox and the bottom chamber by the door as the stove cools down and moisture can condense, especially with a new load of wood. I am using new silicon gaskets and I know my stove is tight.
Another possibility is excessive "huffing" so the steam blows back into the airbox and condenses on the cold metal. I think this causes the water problems under certain situations.
Moisture creation varies greatly during the wood burning process as the Hydrogen components of the wood get burned off first. This means that
a lot of H2O gets created during the first half of the load. Burning wood will create 1.7 lbs. of water for every 1 lb. of wood burned! During the second half of the load burn the wood is mostly Carbon (Charcoal) so the exhaust is mostly CO2 and not H2O. It seems that it's during these initial burns that the moisture issues happen when the load is light, as the water content gets boiled out and the Hydrogen burns create a lot of water as well. The exhaust is mostly steam that REALLY wants to condense on the cold metal parts.
I would think that opening the airbox a crack would cause excessive creosote problems in the tubes, especially if the load on the stove is light, as it would create a draft. It may even cause greater moisture condensing as a small stream of very cold air would be continually introduced. I would not recommend this as a solution.
Is there a way of running the stove heavy for a few days to see if idling is an issue?
What are your temperature settings?
What type of wood are you burning?
How small is it split?
How much do you load the firebox for a 12H burn?
What are your outside temperatures?
How tall is your exhaust stack?
What are your air and fan damper settings at?
Let's see if we can find a place to start troubleshooting.