When I turn off the "Extrude Strokes" effect, all the lines become visible, but the overall result gets a bit messy.
Editor Screen:

Preview Render:

Edit: Okay, I figured out what's happening. Some lines with "dirt" on the face are on the same layer as the head, and that's causing the issue. Is there any way to prevent this? Maybe by making the editor more efficient, like utilizing more of my graphics card to render everything correctly?