Personally I prefer Norton 360 and it has obviously served you well. I have successfully transferred 360 to new computers and the method is to use your Norton Online Account - presumably you already have one of these?
If you log into that account you will see the Licence details for the current one and the number of days left on it. You will also find a download link which you should use to download the latest software to your new computer.
Obviously remove McAfee from the new computer first!
On one occasion I had to "Chat" with a Norton technician to tell them what I was doing and they remotely took over the computer and set up the remaining unexpired licence on the new one. (If the current version of 360 is a 3 licence version and you have spare licenses this probably won't be necessary.)