Let's cut to the chase about this Rabbi Gamalliel's letter, and what it might mean. (See Part 1 and Part 2 if you need to get caught up quickly.) As I said, there are two major oversights in Beckwith's whole argument, one minor and one major.
The minor problem is political and the major problem is economic.
First, the minor problem. It is well established that Jerusalem's local government was dominated by Sadducees before 70 AD, and that the Pharisees rose to much greater prominence only after the Temple's destruction. Thinking about Rabbi Gamalliel's concerns should lead us to question not in which era that letter might have been written, but to ask in which era that letter might have carried weight with decision making authorities. The answer is both obvious and clear. Before 70 AD, Jerusalem's ruling elite had no political reason to change course [as Beckwith's scenario suggests might have been the case] simply due to one Pharisee's opinion.
Now, we must quickly admit, despite this, that Gamalliel's ineffectiveness before 70 AD would not necessarily be a problem for Beckwith's scenario. That such a Pharisee could have felt moved to write such a letter, before 70 AD, is itself reason enough to suggest that the Sadducees could have scheduled Passover too early in some year for that Pharisee's preference. But as I said earlier, this is a theoretical possibility. It's not really a practical likelihood. Therefore, while this first problem isn't technically a problem for Beckwith's argument, it does display a lack of practical consideration about the political reality surrounding such a plea in the pre-70 era. That's a 'minor problem', to say the very least.
But this minor problem eventually leads us to the major problem, which we'll get to in a moment.
There's another angle to question things from, altogether. Instead of asking in which era the letter was more likely written in, or in which era it would have been more likely to carry weight, we can ask more pragmatically, in which era was such a letter more likely to be necessary? Again, the answer should be immediately clear.
After 70 AD, with Jerusalem no longer able to host major festivals, and no Temple to hold the official sacrifice of each family's lamb, the Rabbis had to begin coming up with new procedures for largely decentralized observances. That the Rabbis had not been in charge of this ever before is one factor. That custom in general was now facing upheaval is another factor. Beckwith's Gamalliel letter is theoretically plausible in any part of the first century, but it makes much more practical sense in the post-70 time period. Likewise, in turn, such a letter makes much less practical sense in the pre-70 era, and for this we have several more reasons.
Up to 70 AD, the Sadducees had been lording it over Jerusalem for over two centuries. In the 30's AD - including all possible dates for Jesus' crucifixion (that question being the whole point of all this, remember), the Sadducees had just spent 20 to 25 years managing Jerusalem beneath the comfort of Rome's direct rule. Point being, for the first time in centuries Judea's local government did not have to concern itself one iota with the business of self defense.
Human History has long since revealed that local governments in such situations tend to increase their aptitude for furthering economic prosperity, and they can often do so quite dramatically (the obvious 20th century examples come quickly to mind, but Roman Provincialism also bore this out over and over). The local ruling elite, the Sadducee Party - who naturally included the landowners, the brightest, and the most capable men in Jerusalem - they simply must have spent all of those decades becoming more skillful at increasing both civic and personal revenues. And when you look at first century Roman Jerusalem, between AD 7 and 70, the biggest single source of annual revenue was the festival season.
All this background, finally, brings us to the 'major problem' with Beckwith's proposal:
The Sadducees should have been way ahead of Gamalliel, in any year, because waiting for more grain and fatter birds and lambs, in any year, would have always been much, much more profitable.
In other words, it's a money thing. Duh.
To be concluded...