I did this real quick - I'm off to work - but try putting the object LAST in the
hierarchy so that the CSG inherits ITS texture properties, not the other way
around.

 #version 3.8;
 global_settings {assumed_gamma 1.0 }
 #include "colors.inc"

#declare Aspect = image_width/image_height;

 camera {
  location <0, 5, -10>
  right x*Aspect
  look_at <0, 0, 0>
 }

light_source {<0, 5, -10> color White}

plane {z, 1 pigment {White*0.2}}

#declare Line = 0.015;
#declare LinePigment = pigment {Yellow+White/2}

#declare Slice = 0.1;
#declare Sphere = difference {sphere {0, 0.5 } sphere {0, 0.3 }}
#declare Box = box {<-1, 0, -1> <1, -Slice, 1>}

#declare E = 0.000001;

#for (M, -0.5, 0.5, Slice)
 intersection {
  object {Box translate y*M}
  object {Sphere}

  translate x*M*10
  pigment {Red}
 }
#end

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