The one-pentecontad liturgical cycle having the internal structure (40 + 3 + 7) days is typical for the second pentecontad of several Second Temple period Jewish calendars (40 days after the Pentecost are those passed by Moses on the top of Sinai), whose final feast is that of New Wine. These features are fitting perfectly with the 3 Mac narrative, but the Egyptian dates provided prevent us from accepting this interpretation. Normally, the time of the Jewish second pentecontad has to cover the Summer Solstice (especially important in Egyptian modifications of these calendars), then near 26 or 27 June (Julian), whereas our pentecontad covers some period within July and August (Julian), according to both Sothic movable and Canopic immobile (s. Bennett 2011) Egyptian calendars which were in secular use throughout the 2nd cent. BC (the period to which 3 Mac is to be dated). It looks as if the second pentecontad with its feast of New Wine is displaced to either the original place of the third pentecontad or simply some fixed dates according to the Canopic calendar.
The July–August calendrical setting is additionally corroborated with so far unexplained details of the narrative. The synchronism between the 40-day period of the forcible gathering of the Jews and the Egyptian Payni (= 2nd month of šmw) festivities for Bastet and Hathor sheds light on other details of the narrative. The emphasis on the interruption of the marital rituals of the Jews (4:6-8; cf. 1:19), gathering of the male, female, and children together, journey on the boats (ch. 4) recall, by the contrast, the fertility rites of the main festival of Bastet such as those described by Herodotus (2:60). Moreover, the role of wine and even drunkenness in festivals of Hathor would have contributed as well to the development of the plot of our legend (together with the already noticed there Ptolemaic syncretistic cult of Dionysus). This synchronism with the Bastet and Hathor festivals was probably the reason of shifting the Jewish Second Temple New Wine pentecontad cycle.
Thus, we came to two working hypotheses: the Greco-Egyptian month names design either (1) months of some Jewish calendar or (2) those of an Egyptian calendar (in this case, the Canopic one: the only immobile secular Egyptian calendar; it is mathematically equivalent to the Julian). If the first hypothesis is true, it must allow reconstructing, at least, a part of the liturgical year from the Passover to the third pentecontad festival (the New Wine, in our case, that supposedly replaced the New Oil) within a 364-day per year (364DY) calendar. If such an attempt fails, we have to consider another hypothesis. Fortunately, this attempt does not fail.
The resulting calendar is the following (backward from the third pentecontad):
25.IV–14.V — The third pentecontad (the New Wine replacing the New Oil),
24.IV — the former New Wine festival, the last and the culminating day of the second pentecontad; this date of the New Wine is known from the (Jewish Egyptian) calendar implied in the Joseph and Aseneth (Lourié 2013; cf. Lourié 2012), where the calendar is that of 2 Enoch (30 days in month III, but 35 days in month II).
6.III — Pentecost (festival of the weeks): the date apparently coincides with that of the rabbinic calendar but, within the 364DY framework, with that of the 2 Enoch calendar (shared by the Joseph and Aseneth).
6.III as the date of the Pentecost implies the 364DY framework with the beginning of the year (1.I) on Sunday (not Wednesday, as in 1 Enoch, Jubilees etc.), thus allowing the counting of the seven weeks after Sunday 22.I (the only method of counting that meets all the requirements of Leviticus in their literal sense; s. Lourié 2012).
The Egyptian month names cover the following Jewish months of a 364DY Sunday calendar: Epiphi V, Payni IV, Pachon III.
3 Maccabees, like the Joseph and Aseneth, implies the calendar of 2 Enoch, whereas in a different liturgical representation.
UPD shift of the rite of chalice between the pentecontads: cf. Philo, De vita contmplativa... (my art. on SA).