I messed around with all the various settings and tested them out...took about 20 minutes, but apparently the secret to being able to use any of the ways to mute the phone requires the selection in settings/volumes that is called "link ringtone and notification volumes" to be UNCHECKED.
If checked, if you mute the phone in any way, it will only mute the ringer, and not the notifications. But if you have this unchecked, and select "silent mode affects notifications" at least you can mute the ringer AND notifications.
You just can't independently lower the volume of notifications along with ringtones. Le Sigh