You are correct about the Keystoker power vent arrangement.
A barometric damper would help the Keystoker, but with an IMPORTANT consideration.
On your stove the factory power vent is located very close to the stove top. UNDER NO CIRCUMSTANCE, as Matthaus pointed out, should a barometric damper be installed beyond the power venter in the exhaust pipe leaving the house.
Still, for the problem you are having, a barometric damper would solve it, if you install the damper between the stove discharge pipe and the power venter.
Of course this requires a fair amount of modification to the top of your Keystoker stove.
Sorry for the misinformation in my previous post on this topic, and thanks again Matthaus.