I re-read your post properly, where you said that even the cornices are also turning brown, and I have to agree with
@WAslayer that the root cause is smoke coming out the front vs the flue.
Lots of reasons for this, all boil down to the flue not being able to extract smoke quick enough. So you have 2 options: Make less smoke, or get the flue to extract faster. The latter could be a design issue as well.
Ideally you want the flue to suck all the smoke out, you need negative pressure up top the chimney.
1. Make less smoke: When you start a fire, there is typically much smoke, which indicates improperly combusted fuel. This cause soot in the chimney, and smoke coming out of the front of the braai. You have to slowly add good quality fuel, to ensure near perfect combustion. Using excessive amounts of hard wood in the beginning stages is a common cause, it will smoke a lot until it catches alight properly. Assuming that your chimney and cowl is good, slowly add the fuel, don't just dump it all in one move.
2. Get the flue to extract better: This is dependent on chimney design. A well-designed flue will create a negative pressure at the top (once warm), effectively sucking all the smoke out of the chimney. If it is well designed, you can help it with a good cowl, or even adding a wind-driven device. I have seen some poor chimneys, as well as some really poor "budget" cowls, some that are welded / rusted in one position and do not even turn in the wind. Chimney design matters too: All too often there are twists and turns in a chimney, all which reduce effectiveness, as well as differences in chimney diameter / size. Straight up is best if possible, with no kinks, and an even diameter. And a chimney also needs to be high enough for the cowl to catch a wind.
