It turns out I was being too clever. My onion rings didn't look like the picture. The stitch count was off and the rings wouldn't lie flat.
The pattern clearly states "Work using 2 shuttles". Onion rings with two shuttles are done by working the center round as a normal ring and the outside rounds as a series of chains.
Here's the final butterfly, with two shuttle onion rings. I think it looks better. It certainly lies flatter. So, perhaps the moral of the story is: It's more important to read the instructions than to use clever techniques :)