It would still be difficult to build up a carbon monoxide...

It would still be difficult to build up a carbon monoxide concentration with a blocked flue, as soon as the slow combustion heater door was closed the fire would die because it needs the airflow up the flue to draw in oxygen. If you left the door open things would quickly become so uncomfortable from smoke buildup that carbon monoxide poisoning would be the least of your worries.

It is an excellent policy to clean the flue at the start of every winter, I have never seen a flue fire but I have heard it is a nasty experience caused by a buildup of unburnt wood tars that have coated the inside of the flue igniting when exposed to hotter than normal flue gasses. Something to look out for after the flue has been cleaned is a pile of ash and tar flakes piling up in the top of the fire box and blocking the air flow from the fire box to the flue, that will have exactly the same effect as a blocked flue and it can be very confusing until the problem is found.