Moresnow now has a BK, so he's probably seen me mention the ash-clogging problem a few times in the annual BK stove threads. It has affected just a few of us with taller chimneys on BK 30 boxes, as they seem to have a pretty aggressive air wash system, by comparison to the older BK's.
Your chimney is shorter, and you're not burning on high, so you'd think that maybe your problem is different. But, depending on the stove design, maybe it's still the same issue, the air wash stirring up minute (invisible) amounts of fly ash. Over weeks and months, this becomes enough to plug the cat.
The only other thing I can imagine is too much time spent burning with cat below active temperature, such that it's plugging with unburned fuel. You're seeing it as ash, maybe because you later got the combustor hot enough to burn up whatever had been previously deposited during a cool phase, leaving only ash behind?