twisted brioche stitch in the round

I wanted to do some brioche stitch as a decorative hatband, so had to figure out how to do it in the round.  I decided to do the twisted brioche stitch found here.  I also did one with the top Tunisian brioche found here, but that was simple.  The twisted brioche is a little more difficult partly because it becomes a repeat of six rows instead of just three.  It is also expressed in a style similar to using a "yarn forward" followed by knitting or a "yarn back" followed by purling when what is actually desired is a simple "yarn over".  It's the third row that is particularly problematic.

Anyway, with my interpretation of the instructions translated to in-the-round, done with Caron Simply Soft on #7 (4.5 mm) needles, this stitch looks like this:

Abriviations:
yos1 = s1yo = slip a stitch while doing a yarn over.  This results in a pair of stitches in the same spot which is common to brioche.  They are usually knit as one on the next row.
k2tog = knit two together
p2tog = purl two together
k = knit
p = purl

Instructions (requires a multiple of 3 stitches):
1) yos1, k2tog (repeat these all the way around)
2) p2tog, s1yo
3) k1, k the yo but leave it on the left needle, k2tog (yo and stitch)
4) p2tog, s1yo
5) yos1, k2tog
6) p2tog, catch the yo with the left needle and p it, p1