Welcome to the board. I know it's not much of a suggestion, but I would just go with an edge to edge panto type quilt file. I would choose one of the medium colors used in the quilt for the thread. An all over won't pull your eye to a specific place on the quilt, preserving the piecing design.
If you are thinking about doing each section individually, you would probably have to program a design to fill in the "L" shaped space.
Last edited by PaperPrincess; 03-05-2016 at 09:52 AM.