Could be done with a painted shader (stupid me, why didn't I think of that before?).
Just paint on the plane, make the middle white with drop-off to the edges, attach as blending, invert blending..
But where to apply the blending? At the opacity function powerfractal, it doesn't work.
Adding a second distribution shader for the default shader, applying the painted shader as distribution to that and plugging that as input into the first distribution shader doesn't help either.