You have said that Eire is a British English word - I would like to know what is means. Can you quote a dictionary definition for me please. I don't think that is too much to ask, do you?
I am also puzzled by your logic in your next point. Lets take Eircom as an example - Can you point out to me where in it's branding it uses either the word Eire or Éire for that matter. I would be interested in seeing where the Irish Government uses it and in what context.
Did you have a look at the boards thread I linked?
As for the BAA and their use, well, I think as country we have a lot to be embarrassed about. I think our treatment of Ireland has been particularly shameful throughout history.
EIRcom.... EIRgrid.....
Both for example incorporate EIRE into their corporate identity, primarily their name.