Can Apple Watch faces display reminders other than the scheduled list? Some of the faces available for the Apple Watch 4 allow me to set "Reminders" as one of the displayed complications. Unfortunately, all it ever shows is "NO REMINDERS" because none of my reminders are scheduled.

I can't seem to find any settings at all for the Reminders app, either on the watch or in the iOS Watch app. I just want it to show me the top item in a particular list. Is that possible?
No, you need to have your reminders scheduled to show on the watch face. 
To workaround this you can simply set them for a date long in the future and set the alarm to no alarm.