[Freestyle] Smoother curves for low-poly models?

I’d like to use low-poly models for animations because I’m using old hardware. This means I can’t use subdivisioning to solve all my problems. One solution for me would be to have smooth bezier curves output from freestyle, using the vertex points as guides rather than the face edges needing to be strictly followed. (Don’t worry about the color fill. Yes, there would be gaps in the Blender render itself but I can fix that.) Alas, this doesn’t appear to be possible.

Looking through the documentation on Freestyle:
It appears as though it isn’t possible to alter the course of the line and make it smooth. In fact, once it enters the Freestyle pipeline, you can’t modify the number of vertices at all to manually smooth out the line.

I’ve tried toying with all the settings is Blender to no avail. The best I can get is rounded edges around vertices.

Is there any way to do this without gutting Freestyle?

Edit: To be clear, I mean the kind of effect where if you rendered a square, it would have the stroked outline of a circle.

Side note: I wish BA wasn’t such a pain to post topics in. Slow JS. Why so much JS??