How to stop phone calls from ringing on every device?

Turn off calls on other devices.

EDIT: I didn't read far enough to get to the end of your post. Glad the one thing is done, but here is my look at the other. Not positive on it, but you can decide what you may want to try.

I'm looking at mine, and my MBA is only listed once. To my understanding, that listing is based on the sign-in of the Apple ID. I'm not so sure about changing a password to make that change though. I'm quite new on the MBA, so I don't know a lot of the little things you can do, but when looking at the support document about text message forwarding, How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support, there is a section for if you can't see that command on the phone.

* Don't see the Text Message Forwarding setting on your iPhone? Go to Settings > Messages, turn off iMessage, turn it back on, tap Send & Receive, tap Use Your Apple ID for iMessage, then sign in with the same Apple ID used on your other devices.

I just wonder if turning that off and then back on again would reset that list? I'm just guessing here based on the fact it would seem to reset the phone portion, if you wish to try it.

I'm glad you were able to get it sorted out.