I found where I left my moisture meter and got out my Fiskars. I tested 4 pieces that were straight enough to re-split easily and read between 16% and 24% moisture content. So some of it is definitely still too moist.
Does burning this stuff damage the catalyst? The stove used to cruise in the active zone easily. I would expect the same, even with slightly moist wood after all the water is boiled off, but that isn't happening.
I don't think it damages the catalyst - UNLESS you engage it before it is up to proper temperature. That would result in clogging it with creosote. I'm not sure whether it is possible to get that out - if yes, it's not a damaged cat, but a cat in need of cleaning. Others here will surely chime in.
Note that if you burn wetter wood, the heat available to heat your cat to active temps will be less (b/c quite a bit will need to be used to evaporate the water). Therefore, if you have a routine ("burn on full for X minutes, and then engage the cat") that might not be sufficient. I.e. read the cat temp gauge as that won't be affected by the water but just read the temp (and tell you it'll take longer for the cat to get up to active temp).
So maybe your cat is partially covered in creosote - i.e. a part of it is not functioning as it should, not generating as much heat initially to help light it up (the initial heating is an avalanche in that it heats it up from hot gases, gets some active parts with local heat production, that heat up more parts leading to more heat production etc).