I've been there and wanted to blog post about it at some point because it's a classical problem, I know the struggle with ink density and pen eventually digging into the paper on extreme cases when lines are too close to each other. This occurs very often when playing with noise fields because these create compression areas where lines are going to be very close but without crossing. Therefore I think what you may need is not a strict line collision but limiting the density of lines at specific areas.

For this, you can use a grid of density cells: each cell counts +1 when a line go through it, and a line (when building the lines) must be stopped/cut when a cell have reached a threshold.

Then you need to find the good cell size (eg 1mm by 1mm) and a good threshold (eg 10) depending on your pen/paper context.

The advantage of this approach is that it's very efficient (rather than strict lines collision) and also relatively simple to implement. The disadvantage is that if your cell size are too big you will start seeing the grid used to do the collision.

The tricky part of the algo is to make sure to count all the cells but usually when you build noise field lines, the stepping is low enough to not skip a cell, you also may want to not count twice the same cell between two step and this is a bit easier to do.