I figured it out. I just put this on that Widget model:

def delete(self):
    files = WidgetFile.objects.filter(widget=self)
    if files:
        for file in files:
            file.delete()
    super(Widget, self).delete()
This triggered the necessary delete() method on each of the related objects, thus triggering my custom file deleting code. It's more database expensive yes, but when you're trying to delete files on a hard drive anyway, it's not such a big expense to hit the db a few extra times.