Wexflyer I support what you are saying. From common usage in the north, members of my family called themselves Anglicans from words 'Church of England' (anglo is a prefix).
I don't think they saw themselves as different from people attending Anglican churches in any place around the world where we have our own Bishops/rites in some cases. Altough clearly there was a point of pride in having Irish 'Anglican' bishops. In NZ we call ourselves Anglicans even though we have NZ Archbishop/bishops etc.
In my limited experience the greater difference in protestant churches in Ireland is between CofI/COE whatever you call them, and the Presbyterians rather than branches of the Anglican church in Ireland, England, India, Australia etc.......