A version of Anhrán Mhuighinse is published in Tomás Ó Concheanainn, "Nua-Dhuanaire III", Dublin: Institiúd Ardléinn, 1978 (reprinted 1981). The sources are Béaloideas 1311,367-9 (Carna) and Stoc, Jan. 1925
In Béaloideas the song was titled "Amhrán Mháire Ní
Chlochartaigh" and the story was given much as above, from the telling of Éamann Ó Conghaile of Árd Thiar, Carna. Parts of this song are also found in another lament called "Bríd Ní Ghadhra", published in Stoc, Jan. 1925 and also in T. Ó Ceallaigh, "Ceól na n-Oileán" (Dublin, 1931 – and I believe recently re-issued by Cló Iar-Chonnachta)

Brian, there's also a song in Nua-Dhuanaire III called "Taimín Bán".