IMO it's imperative that you use only very light pressure with the Sharpmaker or any similar v-sharpener if trying to get a very fine edge.
This is especially so if you're using the corners, but also using the flats. As you point out it's difficult to keep the edge on the flat .... just the slightest bit of left-right error in the way you hold the blade and now you're sharpening on the edge of the rod's flat side which makes for a very small area of contact and thus potentially a great deal of pressure on the edge. If you look at the way metal is left on the rods when using the flats you usually see a lot more at the edges of the flats rather than in the middle, which tells you this is what's happening .... also I've found some Sharpmaker rods where the flats aren't flat, instead a bit hollow (and irregular) in the middle.
All of which supports the conclusion: never use heavy pressure when using a Sharpmaker or similar, and continue to use lighter and lighter pressure as you get closer to the finished edge you want. The last few strokes I make are so light you would think no metal is being removed at all - it could be that this burnishes the edge as much as anything - but the difference in sharpness this makes can be huge.