iCloud, created @me.com email with wrong Apple ID, how to claim it with correct Apple ID?
If I understand correctly, you would like to change the primary email address associated with your apple id, this is not only possible but fairly easy to do if you have the right site. 

Click "Manage your account" about halfway down http://appleid.apple.com and you should be presented with an option to edit "Apple ID and Primary Email Address".