I love the concept of the Southwest parishes highlighted. Instead of the box, how about highlighting the specific parishes. You can identify the parishes by go-ogling Louisiana map by parishes. The perimeter would be the state line on the west and south and the north perimeter parishes would be Beauregard, Allen, Evangeline, St.Landry to the east would be St. Landry, St. Martin, Iberia and St. Mary. If you put stars on the logo, please place the number of stars that represent the number of parishes included.
As an option, you could leave the box. Just make sure that it follows the relative border of the parishes I've stated above.