Toon Texture Map Problem

So here's the model I'm working on:
I'm trying to go for a shading style that mimics arc-system's art style. Similar to this:

I'm working on texturing the 'Inner Lines' that Sol's got on his deltoids. From the GDC talk that Junya did on the subject, they seem to use intersecting polygons to mimic an outline. Like this:



However, when I try to achieve this look myself, it comes out blended, like this:



I've taken a look at the texture map I'm using. The texture map looks like this:



Which looks the way I want it to, but when it's applied to the model, the UV map looks like this;



It gets weirdly digitized on the black part of the UV map.

I've tried using Jpegs, Tiffs, Bmps, Targas, and all of those seem to have the exact same problem.

And if I bring the UV shell to the right side of the yellow square, I still get the same blended line problem:



Anybody know where I could be going wrong?

Here's the link to the GDC talk I've been using to learn about achieving this style if anyone's interested: https://www.youtube.com/watch?v=yhGjCzxJV3E