i'm getting late on this thread, but good job
don't worry about the draw you'll get used to it, may even like it better. i don't think the draw affects the stropping much, to me it seems to be just a feedback feature.
the benefit of using a pumice stone instead of sandpaper seems to be that the stone surface is flat and it seems to be a whole lot gentler on the leather, compared even to fine sandpaper.
i don't think the debris make too much difference either, as long as they're leather and not sandpaper grits!