If it were me, I’d try the technique we show in our tutorial hemming jeans with original hem: https://www.professorpincushion.com/professorpincushion/hem-jeans-with-original-hem/ Instead of doing this at the hemline, you’re doing it above the embroidered edge. You’ll end up with a straight stitch above it, so maybe do a basting stitch first to see how it looks but, since it’s solid black, it might not stand out too much. good luck!