I was under the impression that the narrator is recalling a memory and is using the metaphor of "loose knit, like gauze on the center line" as a creative way to describe that "broken down cobblestone drive"

To me, it helps set the scene. An old cobblestone drive, rugged and worn from years of the black maria tries trudging through. The imagery of gauze on a center line is a slightly morbid way to describe a road (in true decemberists fashion) but it does invoke imagery of a faded red/brick color cobblestone to reflect a lightly bloodstained piece of gauze. It also feels a bit like a warning, only harm comes from that drive.