Just a quick thought, can you edit the sketch of your second cut to take up the area you want to remove? Just offset what you need from your other sketches and you should be able to get the profile you want. Then make a line collinear to the top and bottom edges of the flats and trim to that.
Thanks for the Suggestion! This works, but I prefer the second answer since it involves a little less additional features.
the source of your problem is that the sketch for the wrap extends above and below the ring - either make the ring taller, or the sketch shorter so that they line up and wrap6 wiil do what you want.
2 other pointers:
fully define your sketches whenever you can
keep your sketches as simple as it is reasonably to. - I would wrap the center section, then wrap one instance of the pattern next to is, then use a circular feature pattern do do the rest of the ring.