Looks like there's a simple trick that works pretty well. I use the hair I originally used and just reduce the x scale and the y scale. This will slightly reduce the volume of the hairstyle. I move bangs over the face by morphs. I slightly increase the number of collision iterations so that the hair will fit to the head. I still have to play around with shaders, colors and the opacity map, but I think the first attempt with this approach doesn't look that bad. Maybe I'll make a few minor adjustments with a mesh grabber or geometry editor.