I don't have the answer, Lynn, but can only offer what to me seems like a pretty good source for a profile completely lacking in sources or documentation. It has two volumes, so I link both of them here. I did try to find the answer but failed, and I'm probably not the best one for the job.
"Irish Pedigrees; or, The Origin and Stem of the Irish Nation" by John O'Hart, John (1915)
https://archive.org/details/irishpedigreesor011915ohar/page/n7/mode...
https://archive.org/details/irishpedigreesor02inohar/page/n5/mode/2up
More information about Eithne Uathach and Aongus MacNadfraech, King of Munster, on page 70 of the text.
https://archive.org/details/irishpedigreesor011915ohar/page/70/mode...
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Googling "Óengus mac Meicc Eircc" led me directly to Óengus mac Nad Froích on Wikipedia, where it states: "He was the son of Nad Froich mac Cuirc by Faochan, a British lady (called daughter of the King of Britain).
I think this "Nad Froich mac Cuirc" is actually our 'Óengus mac Nad Froích'.
https://en.wikipedia.org/wiki/%C3%93engus_mac_Nad_Fro%C3%ADch
References
Notes
1. all dates per The Chronology of the Irish Annals, Daniel P. McCarthy
2. O'Keeffe, Book of Munster
3.G.Keating, History of Ireland
4. AU
5. Chronicum Scotum
6. Annals of the Four Masters
7. Meyer, p. 113–117 (sect. 15–17).
8. Plummer. Bethada Náem nÉrenn vol. 2 (1910) http://www.ucc.ie/celt/published/T201000G/index.html
9. Mary Jones Celtic Literature Collective http://www.maryjones.us/ctexts/kieran.html
10. Early Christian Ireland by T. M. Charles-Edwards
11. G.Keating
Bibliography
Annals of the Four Masters
Annals of Ulster
G.Keating, History of Ireland
O'Keeffe, Book of Munster
Early Christian Ireland by T. M. Charles-Edwards
Meyer, Kuno, ed. (1901). "The Expulsion of the Dessi". Y Cymmrodor. 14: 101–135.
External links
Webb, Alfred (1878). "Aengus" . A Compendium of Irish Biography. Dublin: M. H. Gill & son.
CELT: Corpus of Electronic Texts at University College Cork
CORRECTION: I think this "Nad Froich mac Cuirc" is actually our 'Óengus mac Meicc Eircc'.
Just spelled differently (and apparently on Geni attached to the wrong wife, evidently his own daughter-in-law).
I have a feeling that due to puzzling variations in the Gaelic spellings and a general lack of cohesive attention to the lineage, not to mention the innate difficulties involved in piecing it together -- it has become scrambled.
I think Aengus mac Meicc Eircc is either Corc or the son of Corc. Corc is number 89 in the succession of Kings of Munster, to be repeated here:
https://www.libraryireland.com/Pedigrees1/Heber.php
https://archive.org/details/irishpedigreesor011915ohar/page/68/mode...
I find Aongus macNathfraoch King of Munster as the grandson of Conall Corc mac Luigthig
And I do suspect that Mac Cuirc or Meicc Eircc is "son of Corc". So to me mac Meicc Eircc sounds like "son of the son of Corc".