After burning a couple of dozen of E6013 welding rods, I finally made some progress in writing with 6013. I used approximately 80 amps setting on the welder and 1/8" 6013 welding rod.
The secret that helped raise the letters and made them more prominent, was simply to make two passes. I moved more slowly on the bottom pass and faster on the top pass, so the top is narrower than the bottom.