I have never been able to get a birthed quilt to lay as perfectly flat as a regular binding quilt. Maybe others are more talented than me. When I did this method, I carefully smoothed the layers after turning and still had some slack for some reason and believe me I cut and layered carefully. I finally pinned it as best as I could and machine quilted SITD from the center out in all directions stopping about 2 inches all around the edge. This left the edge puffy and it wasn't too noticeable that it wasn't perfect. Maybe others can give you better ideas if they have had more success.