I do two different things to break up my lines.
Process1. Copy all lines into one layer, give a .5 to 1 pixel blur, make a mask for the lines, on the mask run the pixellate-crystallize filter at 3, click edit-fade and then scroll thru whatever looks goods at the time. This will take out chunks from the lines and, usually on lettering, I will then max out the contrast to make the edges sharp but leaving chunks chopped out here n there.

Process2. For The Butcher map my lines were all a dark brown, I had one of Coyotemax's parchments at the very bottom and very top of the layer stack. The variation of splotches on the parchment gives the faded-out look to areas of the map colors when you change the blend mode and/or reduce opacity. If you wanted to restrict the faded-out look to just the lines then you could use part of process1 to make a mask for just the lines and leave the underlying colors alone.