Nearly there!
By using that link (
https://supportprofile.apple.com/) I was able to get my primary address changed to me.com
Then I went to appleid.apple.com and was presented with a dialog box asking if I wanted to make my Apple ID the same as my primary me.com address!
"Make your Apple ID and primary email address one and the same.
Your Apple ID will be easier to remember, and your account will be easier to access and manage.
Change your Apple ID and primary email address to:
Submit"
Imagine my excitement, only to have it not actually work.
Sooo so close!