Your symptoms sound just like when i plugged my OEM steel cat (due to 'user error' while learning to operate my stove).
If your cat was plugged, it may help to determine whether the problem is from flyash or from creosote, because the solutions are different.
As others have said, if you can get a good look at the front and back faces of the cat, it should give some good idea of what is happening. Also, if you can remember any particularly odd burns of late where something might have gone off the rails and lead to this problem.
Here are my observations from similar experiences from my BK Ashford. Not 100% familiar with the King, but I assume the theory of operation is similar enough to be a good reference.
Plugged from fly ash:
--You'll often see the buildup obscuring the openings on the front of the cells. As you've turned up the controls to compensate, you increase the velocity through the adjacent areas not blocked, often leading to more fly ash being sucked into the cat.
--BK manual suggest lightly brushing the face of the cat and a vacuum 'near the face' of the cat.
--I believe that at least once i've made this situation worse by vigorously vacuuming the face of the cat clean only to suck fly ash from the flue (and bits of creo flakes that fell down the stack and incinerated in the cat exhaust stream) from behind the cat against the back face of it due to vacuuming the front.
--(If you have a new cat gasket), you could pull the cat, give the cells a good inspection and gently tap it while you vacuum both sides to loosen. DO NOT stick anything into the cat cells to clean them. You will do more damage than good!
Plugged from creosote:
--I once had a burn during an oddly warm day (low draft) and with a load that had a few pieces that must have been MUCH wetter than I realized. I turned it down too low for that quality of wood and left for a few hours. The fire died on me, but not before drawing a LOT of damp, sticky smoke through the cat. The firebox had a coating of gross, sticky creo, which is not entirely unusual for a low burn. But the face of the cat and the internals of the cells were also gummed up.
--When i closed the bypass, the cat was gummed up enough it would stall the fire, just as you're seeing, regardless of thermostat air position.
--when I opened the bypass back up, the fire would come back vigorously.
--I don't know if i read this or came up with it out of desperation on the spot and would NOT recommend it as anything other than a 'what worked for me' scenario...but, what I did to burn the clogging creo deposits off the cat was the following:
--Got a fairly brisk fire burning with your best/driest wood in the front half of the stove with the bypass open. Not a huge load of fuel in case it didn't work, as I didn't want to have to burn a load with the bypass open nor smoldering through a full load with the bypass closed.
--when the flue is warm enough to have a good draft with the bypass open and the cat showing it is heated up (via the cat thermometer), i started to feather the bypass door shut.
--I varied the between holding the bypass partway closed for ~30-45 seconds and then back to fully open to let the fire regain some strength
--after a few attempts i was able to hold the bypass closed a little more and a little longer.
--after 5-10 minutes of this, i had burned enough of the junk out of the cat that it was able to flow enough to not snuff the fire. From there, burned it HOT to get the cat temp up and burn out more of the deposits.
--the idea is that you are feathering the bypass open and closed, alternating between the bypass open and the fire able to get enough draft to burn well with some times of partially or fully closed bypass to pull super-hot exhaust against the cat to burn out the creo built up in it.
--once you get it burned clean, be sure to vacuum it out when cool, as the burned out creo likely left some fine deposits within the cat cells
**this worked for me. I'm not advocating it as a best/easiest/safest solution. i knew i had creo in the cat and had checked and swept my stack and was sure I didn't have a dangerous accumulation of creosote in the flue before getting a hot fire going to try to burn out the cat. If you snuff it down too low, you could get some serious volatile smoke built up in the firebox that could backpuff when it gets enough air. I didn't know of a better way to clean the cat and didn't have a spare. The manual says "TIP: A nice hot fire will usually prove to be the best method of cleaning the combustor of deposits." so this seemed like a viable way to do that.
The fact this came on suddenly to you sounds like what happened to me with the creosoted-up cat. If you happen to know you had a burn that might have smoldered a lot with an inactive cat, i'd look into this.
Mods and those with more experience, I feel what I did above was done in a controlled and safe way (as i tried to emphasize above), but if you feel this is the wrong way to un-gum a cat, please let me know and i will edit or remove the post as I don't want to be spreading bad information.