Now, at last, here's the major problem with Beckwith's proposal that Passover might have been one month earlier, sometimes, than we've tended to retroject when looking at lunar cycles. (See Parts 1, 2 and 3 if you're missing the details behind that statement.) To be simple about things, winter parties are smaller than spring parties, and bigger parties bring in more spenders. Yes, that's the whole point, but it certainly requires fleshing out in much greater detail.
Here, then, is the single most practical point.
The capacity of the festival season to bring in revenues depended on the ability of the Sanhedrin to maximize pilgrimage, and that required the Sadducces to provide at least one simple, reliable, logistical necessity: scheduling!
To make the case with one famous example: Simon of Cyrene would not have been able to attend any festival that was in danger of being moved back by a month, for any reason at all, let alone because some Pharisee said the growing grain suddenly looked like it was fattening too slowly! [We can probably clock that with more rigor if somebody helps me with ancient Judean agriculture. For now, I'll admit I don't know how early the grain heads would sprout, or be measurable by, but for now we hardly need such precision in measurement. If Simon needed a month to get to Jerusalem, and the Sanhedrin needed a month before that to get word out of the schedule, then the Sadducees would have to reach final decision no later than three months before the latter moon Passover, and that's cutting it too close to maximize revenues, if you want pilgrims staying in town one or two weeks before the big feast day itself. And again, why? So they could have a cold festival?]
In short, the Sadducees would not have left such major profits to revolve around Pharisaical whims. We should be almost certain, I think, that after decades upon decades of hosting the festivals, especially after 7 AD, they should have arrived at the logically most business savvy decision. The festival had to be scheduled for whichever of the two viable moons gave them the greatest potential for both travel and ancillary sales. Pilgrims move better the warmer it gets. Doves sell better when fatter, relatively speaking, in any year, good or bad. And even if a pre-70 Gamalliel argued in a very extreme year that Passover needed to be pushed to May, we can absolutely expect that the Sadducees would have ignored him. The ideal month was late March to mid-April, partly because they'd prefer to keep Tabernacles in the moderate season as well, but mainly because the festival had to be scheduled and announced well in advance, in order to attain maximized (say it with me, now) profitability.
With this as our final analysis, one can easily look over a calendar of dates for the entire first century and predict which full moon would have been preferable for the Sadducees from a profitability standpoint. No, the Metonic Cycle wasn't around yet and the equinox 'rule' wasn't an officially documented requirement, at least, not that we're aware. Nevertheless, we should have no trouble concluding with that Passover in the first century should have always been scheduled after the equinox.
The bottom line now is their bottom line then. Scheduling Passover was entirely about revenue.
In 2001, Roger Beckwith did a magnificent job of detailing the intricacies of ancient intercalation, and for bringing such rigor to our awareness about such historical details, he is still very much to be commended. Unfortunately, Roger's blind spot was in failing to see the inevitability of convenient intercalation. It isn't what the calendar might have said that we need to be skeptical about. Rather, we should put our historical faith in what Jerusalem's upper classes needed that calendar to say, just in order to keep the whole thing going year after year, not to mention earning enough to pay for that giant Temple rebuilding project that was (apparently) still underway.
Jerusalem's calendar needed to say, "Open for Business", and it needed to say so many moons in advance.
For more of my (earlier) writings on these points, see the following posts:
Dating the Crucifixion: Sadducees, Calendars and Festival Finances (Nov '09)
Dating the Crucifixion, Despite Lunar Details (Nov '09)
The Passover Travel Itinerary of Simon, from Cyrene (Aug '11)