You can adjust two variables to trade precision for performance:
Samples is the number of angles the outline will render at, around the sprite. The more samples, the smoother the outline.
PrecisionStep: The outline renders multiple passes that are each a tiny bit closer to the sprite in order to prevent holes in the outline. The lower this value, the more passes will be rendered, and thus the less performant the effect is.
Basically, you want to have as little samples as needed, with as big of a step as needed for best performance.
You can't render more than 256 samples, and the shader will not render more than 1024 passes (aka an outline width of 1024 and a step of 1). Turns out C3 will crash before it can ever have the chance to do that anyway so it's all good :)
Thanks to Mikal for his help with fixing the outline's size not always being correct, and fixing the issue where the outline would disappear when another effect was applied beforehand.