That is a good summation. Basically you need to improve draft in mild temp conditions. The extension in height should not be done with single wall pipe. That will cool down the flue gases excessively. To do this properly the chimney should be extended with either more masonry and additional insulated liner inside or with class A chimney pipe.
One thing you can try is opening a nearby window about an inch to see if that helps the draft a bit.
One thing you can try is opening a nearby window about an inch to see if that helps the draft a bit.
