Silhouette Outline Shader and SpriteRenderer

I have a silhouette outline shader on an object, and I also have some SpriteRenderers set up for visual features.

The shader works just fine, gives me a nice outline. And when I set the Offset to around -16, -16 or higher, all the verts in the middle of the model don't get outlined. Yey!

But! The SpiteRenderers are eaten alive and no longer visible, even messing around with the queue of the outline shader doesn't help.

Is there any way to get a SpriteRenderer to show up in the visual space of the model that is being outlined?