Honestly I think your biggest problem is that you deburred with cork and then went on to go cut something (If I read your post correctly). After you deburr you should go back to your highest stone and do a few edge tailing strokes very lightly. This will leave you with a burr free, stupid sharp edge that should cut most things very well if not everything.
This is the video (one of them) I learned to sharpen with. He starts deburring around the 6:15 mark. http://www.youtube.com/watch?v=ozZF2EgnYm0