Well, there's an even more basic problem to the use of Daniel 4 to interpret the synoptic reference to the "times of the Gentiles". The schema that the Society has inherited from 19th-century Protestant/Adventist eisegesis posits a larger application of the "7 times" of Nebuchadnezzer's madness to a period of Gentile hegemony amounting 2,520 years, and this is reckoned from the destruction of Jerusalem in the 18th year of Nebuchadnezzer (the banding of the stump with iron). But this would posit Nebuchadnezzer, the very Gentile who destroyed Jerusalem in that year, as the symbol for God's kingdom that is overrun by Gentiles (i.e. including Nebuchadnezzer himself). This amounts to a very confused attempt at eisegesis.
As for undercover's observation that the Society uses a year of 360 years to compute a 2,520-year period of 365-day years, this actually oddly enough has a biblical basis. The Society plugs in their values for the "7 times" with help from Revelation 11:2-3, which refers to the Gentiles trampling the holy city for 1,260 days, specified as a period of 42 months. This is based on the "3 1/2 times" of Daniel 7:25, and is influenced by the 1,290 and 1,335 days of Daniel 12:11-12. Now, the 3 1/2 times of 7:25 corresponds to the "half week" of Daniel 9:26-27, i.e. 3 1/2 times equals 3 1/2 years. Now all of this is based on the old Zadokite solar calendar, not the lunar calendar that is still used by Jews today, and this calendar had a symmetrical system in which the year was 360 days in length (with four seasons containing 3 months of 30 days each), interspersed with 4 equinoxes and solstices which did not count as days of the month but served to usher in the seasons. So in a month-by-month reckoning, the solstices and equinoxes are omitted. So the year has a total of 364 actual days, but only 360 monthly days. This system was especially useful for sacerdotal functions because 364 is evenly divisible by 7, so the year would have 52 weeks and every year the sabbath and the festivals would start on the same day of the week. Of course, 364 days is one day shy of our usual 365-day calendar, and to adjust for this, there was likely an intercalary "leap week" every 7 years (this is likely the origin of the sabbatical year in the OT). So within this system, 3 1/2 years is reckoned to have 42 months (each month containing 30 days), amounting to 1,260 monthly days, or 1,260 "official" days of the year. There was actually a big debate within Judaism in the second and first centuries BC on whether the 4 solstices and equinoxes counted as official days of the year or served only as markers of the seasons (see the Qumran calendrical texts, Jubilees, and 1 Enoch for some of this discussion). But Revelation has it right, in that 42 months contained 1,260 days. The actual length of the period of 42 months however was 1,274 days when the solstices and equinoxes are added in, and if a "leap week" had occurred within that 3 1/2 year period, the length would be 1,281 days. Note also the 1,290 days and 1,335 days of Daniel 12:11-12, which make perfect sense in the solar calendar. The first figure is 3 1/2 solar years + an extra 30-day month, while the 1,335 days is 3 1/2 solar years + 1 1/2 extra 30-day months (i.e. 45 days). These figures, like the imitation in Revelation, ignore the solstices and equinoxes which lay outside the monthly reckoning. The 1,150 days of ch. 8, however, give a strictly day-by-by reckoning of the first part of the same period starting from the fall equinox to the cleansing of the Temple on Hannukah, and count by the number of times the sacrifices were not given in the Temple, and thus count the solstices and equinoxes. The 1,290 and 1,335 days surpass the cleaning of the Temple and refer to events expected to happen months later (or 3 1/2 years later, depending on how 12:12 is interpreted), i.e. the death of Antiochus and the resurrection of the dead.
Anyway, the basic point is that the 2,520 years that the Society computes is based on a solar calendar that is used in both Daniel and Revelation, but this monthly reckoning of days (used by the Jerusalem priests) intentionally omits the solstices and equinoxes as well as the sabbatical year intercalaries (7 days every 7 years, to amount to an average 365-day year), because these were not days contained within the months and seasons. Thus, the 34.5 extra day-years are accounted for, these are the solstices and equinoxes and sabbaticals that must be plugged into the monthly reckoning to get the actual day-by-day total. Of course, the Society has no knowledge at all of the ancient solar calendar (as they do not read and follow the critical literature on the subject), their fidelity to the ancient method of reckoning is purely an artifact of their use of Revelation to interpret Daniel.
