You need to set you region as USA and language English than in settings go to the app section, choose cortana and switch it on.
I just restarted the phone and still no cortana.Check it, maybe you did not restarted after region or language change.. ?
I have a polish version of 1020 and there is Cortana. You don't need to delete english Englishjust touch american Eng and chose "move it up"....