This is only a partial answer that will create random trails (as open paths).
You can start by drawing a circular arc covering the angle you want (about 80 degrees in your reference picture). Use snapping and ctrl and shift so that the center of the arc is your center point (I used 2 guides for the center point instead).
Then select twice to get the rotation handles, and drag the rotation center to your reference rotation point.
Now use the "create tiled clones" tool to create lots of random similar arcs: Select the number of rows and columns (you will get rows times columns random trails). Then select
-100% as shift X per column and shift Y per row, so that all clones maintain the same center of rotation. Then select
100% as random shift X and random shift Y (this keeps aspect ratio). And
100% as random rotation. Click
Create and this will give you a random set of arc trails, all covering the same initial angle (which you can later change in the original path if you wish).
Color randomization won't work on strokes, only fills. So maybe you can turn your original stroke into a closed path with no stroke paint and a color fill.
You can also control blur randomization when doing tiled clones.
Vaguely related, there is a tutorial from Logos by Nick for blending shapes into curves. This technique creates a gazillion copies of the original, but may suit your use case.