Hi John,
You’re on the right track. Yes, use the difference menu option to create your cutout shape. To fill a “funny shaped” path with lines, you may have better luck with the Hatch Fill extension, rather than the squiggly hatch; it handles a wider variety of shapes.
If that’s still not working, try first selecting the shape, and then filling it just with a solid color, to show you where Inkscape thinks it should be filled in. That might help you figure out if there’s a bigger problem with the shape.
