I sucked it up and decided to take the City tour with airport drop off. Our flight leaves 16 minutes before 3pm, which is the recommended time for international flights, but we have airline status and global entry, so we should be fine. In addition, if it's 3 hours and leaves at 9am, we'll get to the airport roughly 15 minutes after the United counters get staffed (that was our experience this week) so I think we're good there.
I'm not wild about being on a bus, but at least it's at the end. And we can always just not go if necessary.