You are exactly right - when we measured over the weekend....from where the stove would sit, to the top of the chimney is like 15ft. We were going to add 3ft above the chimney like most installations recommend!I'd measure your chimney height. Looking at your exterior pic and the height of your raised hearth, i'd bet you are more like 15' max from the top of the stove to the top of the chimney.
Can you maybe add 3 ft to the chimney if needed?