Last summer I had a breakthrough with this project. I noticed that the proper rhymed office of St Magnus, as it is found in the Aberdeen Breviary (1509/10), the Roskilde Diurnal (1511), the Roskilde Breviary (1517) and the Lund Breviary (1517), is closely based on the office in honour of St Thomas Becket, which was written and composed by Becket's friend Abbot Benedict of Peterborough in around 1173. So close are the parallels, that the greater part of the Magnus office can be (and probably was) sung to the melodies contained in the Becket office. This is rather fortunate, since the printed sources of the Magnus office, listed above, contain text only, whereas there are numerous surviving copies of the Becket office with musical notation.
I know of
The Martyrdom of Saint Thomas Becket by Schola Gregoriana of Cambridge/dir. Mary Berry (Herald HAVPCD 192), 1996 - contains three Matins responsories (Thomas manum, Post sex annos, Ex summa rerum), the complete Lauds, and the antiphon Felix locus.
Memory of Thomas Becket by Schola Hungarica/László Dobszay & Jank Szendrei (Hungaroton HCD 12458-2), 1983 - Matins invitatory, nine antiphons, three responsories (Thomas manum, Mundi florem, Christe Jesu, Jacet granum), the Lauds antiphons, and Felix locus.
Gregorian Chant from Canterbury Cathedral by Lay Clerks of Canterbury Cathedral Choir/David Flood (Metronome B000024G60), 1994 - Matins invitatory, responsories (Studens libor, Lapis iste, Mundi florem, Ferro pressos, Jesu bone), and two antiphons.
UPDATE: There is also this -
O felices lacrimae by Ensemble de Caelis/Laurence Brisset (Studio SM B00006370G), 2002 - first Vespers Magnificat antiphon (Pastor cesus).
Apart from the Schola Gregoriana of Cambridge CD, all these albums are available to stream on Spotify.