Going back and rereading things... try covering the feed. The consensus seems to be some where around 1/4 the opening left open, creating a stronger draw and hotter burn.
With it getting colder at night already and the amount of exhaust you have running low horizontal out and then rising after it has been through the cob run, the exhaust maybe too cool to keep the draft strong. If this is the case whether you want to change it or not , you either need to change the exhaust as suggested or put a blower in the chimney run.
From the top of your riser to the barrel with an 8" heat riser needs around 4-5cm of clearance (maybe 3-5cm) if there is less than that...that may be the problem.
Also the same sized pipe should be used throughout so the fact that you have the exhaust at 5" vs 8" leading up to that certainly may be the issue.
So from what I see. The chimney exhaust may cool too much to create the needed draw. The 5" running may be too small and you may need to remake the run with bigger exhaust( ie 8")...try disconnecting it at the barrel. The barrel may sit too close to the top of your heat riser. In which case building up under the barrel to raise the barrel may help. Simply covering the feed tunnel may help it burn hotter helping the cool chimney problem. Doing this may make other issues more obvious like making the smoke worse...hard to say.
