Well, I suppose you could try blocking the vents, when not using the stove. Maybe look into insulating behind the stove in the chimney. Put a block-off plate above the stove to seal it off from the rest of the chimney.
https://www.hearth.com/talk/threads...ock-off-plate-for-a-masonry-fireplace.147679/
https://www.hearth.com/talk/threads...ock-off-plate-for-a-masonry-fireplace.147679/