I want to change the column order visible when viewing or editing a list item. I have accessed the "Column ordering" interface via the list settings page on other lists in the past, but it isn't visible in this list's settings.
If you have Content Type management enabled for the list (if you see a list of content type with the option to add more), the display order of columns is set for each content type. Drill down into one of them and you'll see the option under the list of columns for that content type.
Change the order of the columns in the list's settings (or the content type)