I would color the white edge with a Fabrico marker that matches the jacket and press it under the edge of the design.
Then I would glue-baste it into place with a tiny amount of Roxanne's Glue Baste It or Elmer's Washable School Glue and applique it with thread that matches the jacket. I would also do a lot of tiny "tack-down" stitches throughout the design in colors that match the design.
Interesting project! :)