Turning Off Messages App Vibration While in a Conversation

I really don't need my phone to buzz every time I get a text message, so I've done my best to turn off all of the vibrations associated with the Messages app. I have done the following:

1. In Settings>Sounds>Text Tone I have set Vibration to None.
2. In Settings>Notification Center>Messages>Alert Sound I have set Vibration to None

After setting both these settings, It's almost working exactly how I want it except for the one most annoying problem of all:

When I have the Messages app running and in the foreground and am in a conversation with someone, if that person replies to the conversation, my phone vibrates. If another person texts me and I do not have their conversation currently open, it does not vibrate!

This is literally the only time a text message will cause my phone to vibrate and it's the main reason that I wanted to turn off all text message vibrations in the first place! Why would I want it to vibrate when I'm currently looking at the conversation as the text comes in?

Does anyone know what combination of settings I can set to achieve what I'm trying for? I just don't want any text message or iMessage to ever vibrate my phone.

I've read both this question and this question which seem related but out of date.

You can make the LED flash instead of Vibrate when you have notifications.

Go to Settings > General > Accessibility and scroll down to 'Hearing' where 'LED Flash for Alerts' resides.

Just go to the search box right when you get into settings and type "vib". "Vibrations" will come up and the first one that u see with the picture of the settings on the left hand side of that line, the first one that says vibrations, and turn it off. If it's green, touch it for it to become grey and turn it off, this is for the iPhone, I don't know about other phones.