Excluding faces/materials from freestyle completely?

I’m trying to use freestyle to outline a simple character with a 2D textured face, and the (mostly transparent) ‘face’ geometry’s outline interrupts the outline of the object it’s attached to, often for some reason leaving a huge gap with no outline at all.
Making that material’s outline transparent predictably just leaves a big gap, so I’m looking for some way to make the freestyle outliner completely ignore given materials or geometry.
I have tried playing around with the ‘Edge Type’ settings. Setting it to exclude ‘Edge Mark’ and then just marking the geometry I don’t want outlined seemed like it should’ve done it, but it didn’t really do anything at all.

Searching around, I’m finding plenty of people talking about how to separate multiple objects into different line sets, but nothing about doing this for parts of geometry in the same object, which I’m fairly sure a character’s face would have to be.
If I could parent a collection to another object, that would probably do it, but that doesn’t seem to be the case.

I’ve also seen people mention using grease pencil instead, but mixed opinions on whether grease pencil can actually replace freestyle. Would it be best to use that instead in this context? It’s important to me to be able to keep the aliased look and the varying line thickness, along with different line colours per material on an object.

In the example image, the result I’m looking for is for that teal line to continue the entire way around the sphere, as it would if that geometry with the star on it weren’t there.
Is there any way to do this? I’m using Blender 3.3, but honestly if a newer version has some miracle fix for this I’ll jump to it.