Hallelujah! That did the trick.
I have no idea how vibrate got toggled 'off' in 'Accessibility', but that was the problem.
When I upgraded to iOS 10, did this setting default to 'off'?
If so, why?
All of my sounds have a matching vibrate pattern, and those survived the upgrade.
I did notice that my personal accessibility settings didn't survive the upgrade. They were wiped out, and I had to reset them. I assume this was because the accessibility settings in iOS 10 were not identical to the iOS 9 settings.
Again, thank you for your help.