Have you tried to remove the door panel and skip removing the door pull/handle step? If it is a solid wood dowel, and there are no screws that you can find, I would think that they screwed the ends of the dowel from the inside of the door panel. This way you could remove the door panel without worrying with removing the handle. Of course this is just a thought, but if I was to put a wooden dowel as a handle, that is what I would do.