After messing with the “in the round” stitches some more, I’ve added a separate page (Stitch Gallery 2) for them.
They’re different because when you do these, you chase the forward pass with the return pass, so you end up with the back side of the return chain.
This changes your access to the horizontal bars (somehow it does, I wouldn’t have predicted this) and can change how the stitch looks.
So if you look at the header, you should see two Stitch Gallery pages listed now.
My new sample swatch looks like this (and has been used in Gallery 2).
These are interesting and I’m still mulling over whether I wish to use any of them in my current project.