I'm not all that experienced with sharpening, but can get an edge that suits me. After a coarse file like what you describe, I go to a finer file like one marked second cut or smooth. That helps take out the coarser file marks. Then, I start with a stone and have used an American mutt for some removal like taking down or smoothing a high centerline part, but mostly an Arctic Fox working with the coarse side then finer side. I use fine sandpaper like 800 then 2000 to really polish it up.
I really like the Arctic Fox over a Lansky.
SwedeFP