Let me say that I don't know if I came up with this myself or if it is a dim memory from somewhere else. I've made several clothesline-wrapped bowls and baskets and have never liked the "taper the end" way of finishing a bowl.
I recently decided to make a new bowl and had an idea. I usually put an accent stripe in my bowls. I decided to taper the bowl off before the stripe and put the stripe on differently. After tapering off the main fabric, I took a length of rope slightly larger than the circumference of the bowl and started wrapping it with the blue fabric. But I didn't start sewing it to the bowl at the beginning - I started about three inches from the beginning of the rope. I continued as normal until I got back to the beginning of the blue stripe. I then cut the rope to butt right up against the beginning of the blue stripe and continued to wrap twice over the beginning of the stripe. That's why I didn't sew the beginning down - it allowed me room to wrap it to disguise where the row started/stopped. Then I finished sewing the stripe down. Then I did the same technique again with the main fabric. Now the tapered end is hidden two rows down and doesn't stick out like a sore thumb.
Another way of describing this is that I ended the bowl as usual, and then sewed a "ring" with no beginning or end on top of it. In fact, I had considered making the ring separately and then sewing in place. But I was concerned that it would be too big or small and not look right.
I know it's hard to tell from a photo, but take a look and tell me what you think. And if anyone knows of this being thought of before, please tell me where you saw it, so I can look it up.