Thanks for the input! I'll have to try a quick turn to re-seat the flapper when this happens and see if that corrects the issue. I was just wondering in an above post if something was getting hung up in the mechanism, perhaps due to slower incremental turning of the thermostat knob. That's an interesting thought about the tension in the coil. I suppose it is plausible that there could be an improperly wound coil or just a manufacturing defect, as my stove is pretty new.
Where the throttle shaft slides through the casting is where it can stick and bind. On a carburetor there are fancy bushings here to support that shaft and a strong vacuum below plus a strong throttle return spring. The BK stat is just a steel shaft in an alloy hole. If you remove the stat cover to inspect this you can easily feel how little spring tension is provided by the bimettalic coil when it is at rest or in a static position. Like open the throttle blade a bit with the knob and then with your finger lightly tap the throttle blade and it doesn't bounce back to to the same place every time. That low strength can be why your throttle blade isn't quite doing the job if there is even the slightest bit of fouling in that throttle shaft bushing area.
CLean clean clean. Then lubricate with something like silicone lube that dries completely because if it's sticky it can accumulate dust and bind again.