Some very, very light edge-leading strokes on the coarse, at a slightly elevated angle can help clean up those coarse burrs. You could also do the very same thing on a medium or fine hone. The important thing is to keep it very light (as if just brushing dust off the hone, with only the weight of the blade and no more). Elevating the angle a little bit will act to bend & break off at least some of the burr, and the light strokes will do the rest by very gentle abrasion (filing it away, in essence). Finish by stropping on some very firm leather or wood, such as balsa. Most of the burr should be removed with the stones; but when it becomes very fine, the firm leather and maybe some SiC or green compound can help finish it off, with the steels you mentioned. Some 1 micron diamond compound also works well, but go gentle with it, as it works more aggressively. It's easier to 'over-strop' with the diamond, which will take some of the 'bite' out of your toothy edge.