240 grit sounds awfully harsh for me, I use that sort of grit usually when I want to remove LOT of steel. I'd use 400 at harshest, unless you really have banged the blade good. Regular sharpening around 800 and finishing with over 1000 and finer the better.
Don't get violent, like mentioned, if you use too much force you ain't sharpening it. If the convex is flat enough, you can just lay the knife on the paper flat like scandi. Usually though, you have to change the angle of the blade so that the very edge touches the paper (or you will be just scratching the sides of the blade). Correct me if Im wrong, but the angle should be so that the edge is touching the paper barely (depending how soft the padding underneth the paper is).
I don't sharpen knives with any other than paper todays. Somehow it's so satisfying and soft way to do it compared to stone. I even sharpen my scandi's with paper (pressing VERY lightly) and I get the best "shaving sharp" results.