Taking a look outside of the burner, Is the issue constant regardless of the weather or are you seeing subtle differences? Aka, does it get worse with breezy weather and stabilize a bit with calm weather? From someone with an old farm house, check the windows, doors, exterior joints, etc and reseal every last one with good caulk if performance seems to fluctuate with the wind. Wind sucks the heat out of an old house quick and will make it work harder, thus eating more fuel.
As to the puffing, pay attention to the wood and weather specifically. If I stuff my fire box on a calm day where its a balmy 28-34 then my stove puffs. The fire has more fuel, is putting out a lot more smoke, and the environment isn't corresponding by pulling a better draft. I blame a not great chimney design. Now on a cold windy day though, I can stuff to the gills without issue. Also, the larger chunks of wood take significantly longer to dry out. It may seem dry on the outside, but it can still have a lot of moisture on the inside, and wood doesn't really dry out when its a round and not split. It may not be the culprit, but it could be part of it
Burning wood is an art form more than anything, and the finer points come with practice and experience. Its aggravating, but it gets better with each passing year.