After completely over-analyzing Mac and iPad writing software, I finally settled on Storyist. I mostly like what I've seen so far.
I dumped some existing text into a chapter, created a few sections, and it's worked fine. The section names seem to be the default ones used when I pasted my text into the existing sample text, things like "Start Writing!", etc. So in the left pane, I clicked on those sections and gave them new names. Perfect.
However, when I play around with the character sheets and try to add a plot point, and tie it to a section, the section names I'm given are all the old default ones, with none of the new names. Perhaps there's a less-obvious way to rename sections (when I right-click on a section in the left pane, the names are correct). I'm not sure where Storyist pulls its list of section names - it seems to keep the original name no matter the change.