From the posts on the forum, it appears that the cause of the incomplete burn is ash around the edges of the firebox that don't shake down as well as the ash in the middle of the grates.
In the center of the grates, the adjacent grates move in different directions, so it takes only half the movement compared to an end grate, to open up a gap for the ash to fall through to the ash pan. On the front and back and along the edges, the ash accumulates and eventually blocks the combustion air to the coal just above the ash.
Using a stiff wire, or small poker, stir the ash at the front, sides and back, and get it down to the grate where it can fall through. Once the ash is gone the coal will burn evenly all the way across the firebox.
I saw this 'problem' in GregWhite's SF150 last season. We made a small poker with a piece of 1/4" round steel rod. This worked really fast to open up the ash-clogged openings in the front grate and down the sides of his firebox. We used the small poker both from below the grate up through the coal bed as well as from the top down through the ash to the grate. Once an opening in the grate was cleared, lots of fine white ash sifted down into the pan.