Actually I think you've done a really great job. The top edge in particular is spot-on. As far as the woven-in pieces, I think the vertical ones look good. From the picture it's hard to tell how they look in different types of light (natural, flash, indoor, etc). I did a similar thing with my Dothraki top, and originally used off-white cotton cord, and it looked way too bright to me. I took it out and used strong black tea to tea dye the cord to a more weathered off-white/light brown. In my case I think that really helped.
So I think your vertical pieces look good, but tea dyeing them might help tone down the brightness, if that's bothering you. That said, the horizontal pieces jump out at me a lot more than the vertical stripes do, particularly the two lowest ones. The vertical threads look like part of the fabric, but the horizontal ones seem to be more just on top of the fabric. But honestly, I think both are little details that only those of us who have been staring at that outfit for this long will even notice, heheh.