Robin was right: I was not reading the pattern properly. That's because it's written in a rather unusual way; instead of numbering picots, it numbers segments between picots so I was making one too many picots (and extras stitches) in several places! In the end I actually stopped reading the written pattern and just referred to the photo for the right number of picots and where to join them.
I still kept my chain reversed the other way between repeats and I added just a few more stitches to it to give a bit more space between repeats. I think it will work out this time.
It's now lying flat and the shape is good and it looks like the eight repeats will fit just right. I look forward to starting on the second round and I do love the fact that it will be continuous!
Thanks again for your helpful comments.