I think if there's any loose ends, try to tuck them under a loose cross weave, then keep it in place with a small dab of super glue. Be very careful to not damage the underlying membrane. The missus or gf may have a ball point sewing machine needle for use on knits could be a good tool since it's not quite as sharp. Despite the name, it's still pretty sharp, so be very careful.
The twill fabric is fairly good at resisting runs and fraying, so just leaving it alone is a viable option as well.