I currently sync my 4s with a windows 7 pc. I'm getting a mac so I want to change the sync to go to that one. How do I do that without erasing everything on the phone like it does when it tells you you are already syncd to another computer.....
Use iExplorer and rip EVERYTHING off of your iPhone, music, contacts, SMS, ringtones, pictures, videos, etc and transfer them using an external hard drive or a flash drive to your mac
Try the authorize this pc function in the link.
The first portion of the link you provided. Try that. There probably are "easier" ways but there's still a lot of prep work that needs to be done before you transition.