Thanks @NightSky, but I have been setting notifications in the calendar.
I think I have it working now. I'm pretty sure something has failed in the past as described above, but after reinstalling and cross-referencing with @Kottonballs' settings all seems well.
Caveat: I think the testing I was doing to check to see if certain settings changes were taking effect was too aggressive: I was setting calendar events with notifications for 20 minutes in the future. These notifications were definitely not coming through - so it could be that I was setting too short a window for the calendar to sync appropriately in the background.
Yesterday, as a test, I set notifications on a bunch of events throughout the day, then restarted the device. After the restart I added another event with notification that wouldn't have been caught on the initial device startup. All notifications fired, so I'm optimistic that things are all good.