Grease Pencil Material Fill with Blurred Outline

In Grease Pencil, I would like to be able to have the edges of certain shapes within an object be blurry. Unfortunately, while you can set the Influence of a Modifier to a certain material, it seems you can’t do the same with a Visual Effect, including the blur effect.
I can get a blurry outline using the Airbrush but I would like the fill to have a blurry edge. Is it possible to do this?