Why did the Sadducees prefer to have Pentecost always on Sunday? The primary motivation had to be financial. If the one-day long festival starts Saturday night, then wealthier pilgrims who were staying in town (not the poorer ones who camped out in the countryside) had to stock up on supplies and be in their rented rooms before Friday at sundown. The Sadducees stayed in power chiefly by serving the needs of Jerusalem's upper class. For a one day festival, keeping Pentecost on Sunday doubles the minimum revenues that might be expected.
In contrast, the Pharisees wanted Pentecost on Sivan 6th because they cared more about arguing over disputable minutiae. It is this same Pharisaic attitude which characterizes much of the Rabbinic discussion found in the Mishnah and Talmud, and which brings us to the point of this post.
Roger Beckwith's impressive compendium of chronological issues [especially on first century Jewish intercalation] concludes [in chapter 9] that Jesus' crucifixion could have occurred in any year between 30 and 36, except 34. However, Beckwith's conclusion relies heavily on assessments of rabbinic disputes about marking the new year, all of which seem to have come from 2nd century or later. At the very least, such legal perfectionism is more characteristic of the Pharisees, who rose to power after Jerusalem's destruction. And although Beckwith asserts it is "by no means impossible" that the "formula" for these citations may date to before 70 AD, it is very difficult to believe the ruling Sadducees would have cared as much, at the time.
Practically speaking, if Beckwith really expects us to believe his citations reflect standard practice before 70 AD, I have only one question - How could anyone ever have made plans to attend the spring festival? Granted, Jews far beyond Palestine could never set sail in time to make Passover anyway, but Alexandria and Antioch were three weeks from Jerusalem by foot, or two weeks by horse, and pilgrims like Simon of Cyrene might have traveled for over a month to arrive at the festival on any particular date. How would such pilgrims have known when to leave home, if the festival dates weren't solidified until just a month or two before the event?
Beckwith cites Rabban Gamaliel II (surely a Pharisee) who once advised that a particular new year needed to be delayed until the first grains were ripe, and the stocks of turtledoves and lambs were healthier. Beckwith is probably right to argue that the mention of turtledoves marks a principle passed down from before the destruction of Temple, but that itself does not mean the letter was written before 70 AD. Even if it was, we must note that the Rabban's advisement is unlikely to have influenced the Saducees, whose most-valued constituents could just as easily sell out undersized stocks to the captive pilgrims upon arrival. An extra month might fatten up profit margins a little, but not if they lost more on volume. The greater consideration, in order to maximize revenues, was to maximize the size of the customer base.
Since the Sadducees were in charge, earthly concerns must have ruled the calendar. Last minute scheduling would hardly encourage more pilgrims to schedule the journey - even Palestine Jews could lose a month from their schedules for two weeks of travel and two weeks in the city. The wealthier the pilgrim, the more at home responsibilities, the less they might appreciate being held up until the last minute. Besides, how would they have received the news? If a decision was made in mid-February to delay Passover until mid-April, instead of mid-March, some pilgrims would not have heard about it until they had already embarked. This could not have been standard.
If we assume along with Beckwith, for the sake of argument, that Rabban Gamaliel II was a pre-70 Pharisee, a strong likelihood of rejection would most likely NOT have dissuaded him from advising his political superiors anyway. Point being: whenever this citation dates to, it merely offers advice. There is no indication that it necessarily had any chance of being heeded, before 70 AD. In fact, it is more likely to reflect that a group of Pharisees merely made practice of marking their opinions as a matter of course, while patiently waiting until such time as they might finally gain power. Of course when they did gain power, after 70 AD, there were no more logistical obstacles against making intercalation as impractical as their Pharisaic hearts desired. At that point, the Diaspora's need-to-know notwithstanding, the practice of dating the New Year became purely academic.
Furthermore, the contentions of Pharisees were not necessarily on significant matters. To begin with, the Sadducees would never have scheduled Passover for February, and probably not for early March. Beckwith supposes an early spring could have sometimes demanded a schedule change, but the harshness of winter has as much if not more to do with the springtime readiness of crops and livestock. The dates on which new moons happened to fall would dictate what choices were available for the Passover month, and in most years the decision should have been obvious far in advance. A Passover in mid-march might have been debatable, but very early March would be too soon to trust and late April would be too late in any year.
A first century objector, holding Gamaliel's opinion, could not have been writing against a February Passover, because the Sadducees would never have risked making such a ridiculous schedule far in advance. More likely, the letter would stand to oppose a mid to late March Passover, in which case, the financial considerations of the landed classes still favored maximizing the customer base over increasing portion sizes.
An early or mid March Passover could arguably have been scheduled. However, while granting (to Beckwith) that the equinox was not yet an official guideline, the Sadducees would still have preferred scheduling Passover to fall on the warmer of full moons available, as long as that was not too late. Again, practical concerns favored scheduling for late March to mid April, equinox or no equinox. And again, under the ruling class, Pharisaic meticulousness need not have been more than a formality.
Beckwith's major argument boils down to supposing that a first century objector could have argued in 30 AD against a March 8th Passover, or in 31 AD against March 27th, or in 32 AD against March 15th, or in 33 AD against March 5th, or in 34 against March 23rd, or in 35 against March 12th, or in 36 against March 1st. Perhaps he could have, but look again at those dates.
As discussed, March 1st, 5th or 8th are highly unlikely to have been scheduled in the first place. March 23rd or 27th would be highly unlikely to have been postponed. March 12th and 15th might perhaps have been scheduled, as being near to but not after the Equinox, but still the Saduccees would most likely have refused to postpone. [On the contrary, the Saducees would probably have preferred an April 14th to a March 15th (in 32 AD) and an April 11th to the March 12th (in 35).]
Once more, the major point is that the Sadducees would be unlikely to have postponed what was doubtless already expected across mideast Asia. Adhering to legal perfectionism at the last possible minute simply would have been bad business. Just as bad for business would have been scheduling a Passover for February or early March. Late winter was simply too risky, and mid-April was far preferable to mid-March, even apart from the equinox. These considerations drastically reduces the variability of Beckwith's conclusion, brining the balance of questions about intercalation (basically) back to daily record keeping and nightly lunar observation.
On this last point, we should expect the Sadducees would at least bow to tradition whenever expedient (tradition surely enhancing the pull for more pilgrims, and thus for more revenues) and the festival traditionally began on a full moon. Therefore - assuming all other intercalation procedures revolved around making sure that Nissan began on a new moon and that Passover began on a full moon, we are probably justified in following the basic metonic cycles to determine when Jesus was most likely crucified.
Since the only years left in question (32 or 35) do not affect this consideration, the chief options must remain 30 and 33 AD. From there, a chronological study of Christ's public ministry (compared with the start of John the Baptist's ministry) should settle the crucifixion firmly in early April of 33 AD.
One further note, of potential importance: according to astronomical reckoning, 26, 33 and 36 AD are the only years under Pontius Pilate in which the most likely reckoning of Sivan 6th naturally fell on a Sunday. The presence of the crowds in Acts chapter 2 confirms that this Pentecost fell on a Sunday, but - as the Pharisees probably had the proper interpretation of God's instructions to Moses about dating Pentecost - the double occasion of Pentecost falling on Sivan 6th could be seen (by some) as a more appropriate date for the typological "baking of the loaf" that corresponds with the first church's "birth".
Obviously, this last point is theological, circumstantial and potentially meaningless. On the other hand, it may be deeply meaningful. Either way, it is worth noting. At most, however, theologians should only consider it as potential confirmation of a sound historical conclusion. It does not count as support.