We've had long discussions on pit modifications in the past. As I recall, for the style of pit you have (I had to look up a picture on line) one of the primary concerns was adding/modifying the baffle between the firebox and the pit. This was done mostly to even out the cooking across the whole grate.
Some folks have seen fit to add some thermal mass to the pit itself (metal plates, fire bricks, whatever) to help even out temperature spikes.
I can't see the bottom of the chimney from the pic I found but sometimes folks adjust the where the chimney ends to try to even out the temp too.