Sounds like you've got the same chimney getup that I've got. And the same problems. I get the rotten egg stench quite often .. then the screaming CO detector shortly after.
I choked off the combustion air on mine .. but mine is an entirely different animal than what you've got. In other words, what works for me, won't work for you.
I'm willing to bet my pipe probably looks just like that after almost 2 months of burning. Have knocked quite a bit of flyash out of the firetube baffles over the past 2 months. Can only imagine what's in that pipe.
If it gets any worse I may have to break down and clean the thing.