How can I do these bits that are poking out on this herringbone brick material?

I would approach that in the following way.
 

First create a single tile for the ‘brick’ with two layers so that the lower layer is larger than the ‘upper’ and give both a bevel.

Next make that single tile into a herringbone pattern.

Use slope blur fed by voronoi fractal to give those edges variation. You can mask the effect with the inverted tile pattern so it does not impact the upper part of the tiles.

You can add a second slope blur to add smaller edge variations and also add addition grunge on the surface and then add colour etc.

It is the slope blur on the extra tile edges that addresses the issue you describe. I hope that helps

Dave