Two things i can think of that may be going on here. first, you mentioned specifically that "the tip of the knife" couldn't cut paper. The tip is always the hardest part for me in clamped systems like the WS precision. The way the blade is clamped, combined with slightly imperfect grinds from heel to tip can mean at the heel you are hitting the whole edge bevel when you are sharpening, but at the tip you aren't quite getting there.
so when you go to test the edge on paper, you are cutting no issue, but then when you go to use the tip on something specifically after sharpening, you notice the very tip didn't get hit. Try and get a cheap jewlers loup online and use that to see if you are hitting the apex of the edge bevel, or feel for a consistent burr along the length of the edge.
The other, and probably less likely possibility is that you you have a wire edge. I would think that is harder to get with LC200N than it is with softer steel, but it is possible that the stropping/deburring process is just straightening out this wire edge and then when you put pressure on it more than a piece of paper, like cutting a sandwhich on plastic, it rolls that wire edge over. Fatiguing the apex of the edge with some very light passes might help, or that firmer leather it sounds like you are already trying could do the trick.