I've been amazed about a couple of things working with LMF. The first is how it seems to "fill in" scratches and make them go away. The second is how much longer it takes a smoother barrel to brown. Next time I'm not going below 240 on the paper, and I bet Mike is right about simply stopping at the draw filing.
I used 320 on my Lyman kit mostlyto knock down the proud metal around the lettering on the barrel, and in the process took the scratches/milling marks on the barrel to just a little smoother than that on my Lyman production gun. I'm about finished with the process now, and the barrel has really filled in and smoothed. But it has taken a whole lot longer than the buttplate and trigger guard which I finished with 240. AND THEY LOOK JUST AS SMOOTH NOW! And even starting with the barrel not much smoother than the production rifle, there are virtually no scratches visible. Looks much better than the production version.
I'll probably draw file the next one lightly to take care of the raised metal on the barrel lettering, but I'll quit there. BTW- with the proud metal gone around the lettering it really does drop back and almost disappear. I know some guys draw file down far enough to get rid of it entirely, but I sure won't bother. I'm not trying to fool anyone into thinking it's a "real" Hawken, and I can live with the lettering when it's less obvious like mine turned out.