yikes,
An asphalt paving outfit could place crushed rock for you using a dumptruck and a little grader (probably a Huber or Athey, or maybe a LeeBoy), or a Layton box on the back of a dumptruck, or even a small paver.
It would probably be cheapest to rent an open trailer from U-Haul, have it loaded at Glacier on W. Marginal (or shovel the crushed rock in yourself so it doesn't get segregated by careful dumping of a relatively small amount of rock by a relatively large loader), then shovel it out onto the alley yourself, then repeat. Another advantage of the hand method is that you can place the material in the two ruts and potholes in order to save grass/weeds in the middle and on the edges.
If there are no wires, tree branches, etc. in the way, a dumptruck could spread the rock to possibly save some handwork.
If the rock will not be covered by asphalt or concrete, the City requires ledge rock (crushed rock from a rock quarry instead of from a sand and gravel pit). Inch and a quarter minus is probably better than five-eighths minus.
If there is a lot of actual mud (not just dirty water in ruts or puddles), then a base course of what we used to call railroad ballast can "heal" the worst spots, but dunno what the City would think of that.
There are bark supply outfits that stock various aggregates, but they usually do not have ledge rock.
The alley will eventually have potholes again unless everyone creeps along in their cars.