Two apparently incompatible features of the old Celtic Church calendar, namely, some form of a "quartadeciman" Easter computus and, despite this, celebrating Easter always on Sunday, lead to the supposition of the 364-day scheme of this calendar. In fact, such a calendar exists in Iceland where it can be reasonably attributed to the Celtic papar. Both calendars should be identified. The Sitz im Leben of this calendar is to be looked for in a Jewish-Christian milieu in Egypt.
1. An unresolved problem of the calendar of the Celtic Church.
As it is stated long ago, a pejorative "quartadecimans" was used against those who were following the old Celtic Church calendar unjustly, simply as a sobriquet. In fact, the Celts were always celebrating Easter at Sunday, while the true quartadecimans of the early Christianity were blamed, first of all, for their custom to celebrate Easter regardless to the day of the week, and therefore, with no due respect to the day of Resurrection.
Be that as it may, there was something real behind, at least, a part of the Anglo-Saxon Church' invectives and canons containing a prohibition of celebrating Easter at "XIIII lunae". August Strobel (1977) collected an important dossier showing that the Easter calculations based on some kind of the "quartadeciman" rules were really in use in the Celtic Church. Probably, Strobel was the first who appreciated the scale of the problem: "Was aber soll das sonntagliche Fest der Iren, das doch unzweifelhaft den quartadecimanischen Character in Frage stellt?" (p. 242).
Strobel was trying to resolve this riddle rather artificially: namely, presuming that the "quartadeciman" computus of the Celts, although pre-Nicean, was relatively late and superposed to the earlier Celtic custom of celebrating Easter always at Sunday. This resulted in a peculiar calendar of the Celtic Church, whose exact structure remains unclear.
I think that our present knowledge of the late Jewish and early Christian calendars opens some extra ways to approach the problem and to avoid any speculation unsubstantiated by the sources.
2. A way to resolve the riddle.
In fact, there is a possibility to join together two rules that seemed incompatible to Strobel and to everyone who faced the problem above. If there is a liturgical year containing 364 days only, the days of the months will be always fixed to the days of the week (because number 364 is divisible to 7). So, it is quite possible to imagine a calendar where the night of the "XIV lunae" will be always fixed to that from Saturday to Sunday, in a perfect agreement with the data of our sources.
Now we know that such calendarical schemes were extremely prolific in the Jewish matrix of the Christianity and in the early Christianity itself. Their remains are known in the Christian Orient as late as in the 4th and 5th centuries. Such a calendar is still in use in the Nestorian Church of Antioch.
Therefore, it would be rather natural to ask whether the Celts could follow some kind of the 364-day calendar.
3. Old Norse calendar and its Jewish-Christian origin
We do know one kind of the 364-day calendar in the Western world. This is the old Icelandic ("Old Norse") calendar whose origin is obviously not Germanic. The historians of the Western calendars take it as of a probably local provenance (because nobody of them knows any parallel to the Icelandic 364-day year). This is, however, not very realistic. The first 364-day luni-solar calendar appears in Babylonia in the 7th cent. BC as the last fruit of a thousand-year development of the best astronomical school in the world. It is not very likely that it could be invented independently by some Vikings and fishermen in the land of the polar nights and polar days…
After the fall of Babylonia, the 364-day calendar is unknown outside the Jewish world and, then, the Christian one. So, a great scholar of the Old Norse calendar, Gustav Bilfinger (1899, p. 75) was basically right in his intuition that apparently so unfamiliar features of this calendar have ultimately "ein christliches Antlitz".
4. 364-day calendar of the Celtic papar
If the Icelandic calendar is not an invention of the Norwegian settlers, the only possible explanation of its appearance in Iceland leads to the papar, Celtic monastic colonists of Iceland since the late 8th cent. Indeed, there is a synchronism: in 716 failed Iona, the last stronghold of the Celtic "old-calendarists" on the British islands, and no later than in the late 8th cent. Celtic monks settle in Iceland. Such a supposition meets our previous supposition about the 364-day scheme of the old Celtic Church calendar.
Some additional observations may be added to establish the Sitz im Leben of the Old Celtic calendar in a Jewish-Christian milieu in Egypt, close to that of the calendar known from the 2 (Slavonic Book of) Enoch.