Wood is 2 years seasoned and the stuff I'm burning was in my basement for the last 9 months. I also have a heat pump hot water heater that keeps it dehumidied.
Draft is the suspect, I'd like to measure it to confirm or deny it's the problem. I'm not going into how my chimney is constructed. I talked with blaze King about it and they said it was the most ideal cinder chimney with clay liner you could get, it's also 8" square.
Chimney inside the house or out?
Yes any leaks anywhere will weaken drafting as well.
I have neighbours with Blaze kings that tell me you can put your hand over an open flue when the cat is engaged and not much heat is coming out the top where it would go up the chimney. Sounds like your king may not be getting those clay tiles warm enough to start and stay sucking hard. Sealed metal pipe straight up and the Kings work great, but clay tile liner on an outside wall on cold nights and it may be staying too cool to keep a strong draft going. As you likely know, a good draft works best when outside ambient temp is colder than a well heated chimney. If chimney stays cold too, then you have stagnant air movement and weak draft.
I have clay tile liners in tall brick chimney in centre of my house and it still takes a good 30++ minutes to warm my chimney up reasonably well., and my non-cat stove running hot puts lots more heat up the chimney than your King will once you engage the cat.
My chimney is the main reason I decided against a Cat stove, cats would not hold my large thermal mass chimney up at necessary good drafting temps, they are just too efficient.