Your real problem appears to be scale:
I think caused by clipping plane being way beyond what is necessary.
You had it set to 1mm - 1km
###Overlapping faces
My first impression is that you are trying to fix the wrong problem. I suspect that the reason you are using BSurfaces is because you don't know why you are getting scratches. The scratches is a much more interesting problem, and knowing how to fix those will help you in future modelling.
If I am correct, the 'scratches' as you call them, are the result of overlapping geometry, and this results in z-fighting. The scale you are modelling at compared to the world scale will result big enough rounding errors to make this noticeable.
BSurfaces hatching
This is perhaps a little too narrow scope for blender.stackexchange but BSurfaces does come with Blender, so perhaps it's OK to answer.
you need to draw the crosshatch this way.
then adding surface is without issue:
