Chimney Length

I picked up a COS a while ago off of craigslist. I've only gotten to do one cook on it, but I'm super excited about the potential. One question though in regards to mods. I put the measurements into Feldon's Pit Calculator and it recommended a chimney height of 31". It is currently 15". Would extending it make much difference? If so, what is the best way to do that?

The diameter is only 2.5", so that requires more length. I have been contemplating how to make my own chimney that mounts on the end of the barrel instead of out the top, but that might be more work that I am willing to do at this point.