Even if we had a fourth tier title, and I wish we did, I would not equate the ruler over the whole of Ireland as a 'emperor' level tier, for the reasons I gave previously regarding mediatization and subsumation.
For context, Alfonso VII took the title "
Imperator totius Hispaniae", Emperor of All Spain, as various kings tried to assert supremacy over the whole of Iberia, and during their lifetime the Roman Church recognized this title. Even if we were granted a long sought fourth tier level, I doubt we would equate the High King of Ireland with an
Emperor of All Spain or a
Holy Roman Emperor ranked title.
The British and Irish Isles focused map is still within the context of Europe as a whole, and the rankings of Irish rulers should be in line with the rulership tiers in Europe as a whole. Of corse, as I said before, if one were to individually make a mode exclusively focused on the British Isles, then you can do as you wish. Take the Byzantine emperor tag away and use it for the Irish High Kingship if you wish.
The reason Welsh rulers adopted the title
prince was specifically because of its connotations and meanings as an independent ruler by hereditary right.
Brenin had no real meaning in French or Latin,
Prince did. The Welsh princes were equating themselves with the European Prince, whatever the title used, be it Emperor, King, Duke, distancing themselves from the comital rank. A Welsh prince was equal, in this sense, with an English King, who was also described as an European Prince, and this use of language is significant in diplomatic circles. It demonstrates the sophistication of Welsh rulers in adopting diplomatic language which was understood both in Latin and in French, the diplomatic language of Western Europe.