Kosonen,
With the aid from my friend who is a rabbi, and I quote:
"The problem is merely an ancient one due to the loss of the Temple. In ancient times the celebration did indeed begin on Nisan 14th in the afternoon with the slaughter of thousands of sheep and home preparation of meals. But the evening meal, the seder, that started that night, was the beginning of the 15th, and always the start of the Festival of Unleavened Bread. And that day that started at sundown was always a Sabbath. You could not do any work, any lighting of fires, any cooking, even the slaughtering of the lamb had to be done before that moment. With the Temple gone, Jews today merely observe the Passover seder which begins on the 15th, and it is always considered a Sabbath."
He mentioned the verses in Exodus that you pointed out are often used by Fundamentalists Christians to try to teach Jews that they have the "wrong day," which in reality the Temple is just gone and there is no slaughtering of lambs happening on the 14th.
As Exodus 12:18 says, "in the evening" of the 14th, they would begin the "Festival of Unleavened Bread," because at sundown the 15th of Nisan began and Jewish days begin at sundown.
As I mentioned in my previous post, in John's gospel, the author has Jesus die on Nisan 14, the same day the Jews are slaughtering the lambs. The rabbi said this was correct because the Jews would not be outside demanding the death of a criminal on a Sabbath or Passover or any Jewish holy day. The gospel mentions the Jews demanded the rush of the affixiation process of the criminals on the crosses by having their legs broken because the next day was the Passover--and a "great Sabbath," meaning the next day was going to be Saturday, the regular Sabbath and Passover, which is always considered a Sabbath, no matter what day of the week it lands on.--John 19:31.
In other words, stating that Jesus died on "Preparation Day" in the Gospel of John and not on Passover unlike in the Synoptic Gospels shows that the Jews didn't eat the Passover on Nisan 14.
Josephus, who you yourself quoted, described Nisan 14, Preparation Day, in fact the very last one before the Temple fell in 70 CE, and stated that "from the ninth hour to the eleventh" (from 3 pm to 5 pm) 256,500 lambs were slaughtered in the Temple for the Passover meal.--War of the Jews, VI.9.3.
That would not be possible on a Sabbath because people could not prepare a meal on Passover because you cannot light a fire to prepare a meal on a Sabbath, which the first day of Passover always is. (Ex 35:3) Passover, as my rabbi friend says, has to be on the 15th.
That's where the confusion lies.
Again, John's gospel merely moved Jesus' death to Nisan 14 as a narrative teaching device as the synoptic gospels and the Church Fathers agree that Jesus died on Nisan 15, Passover, and that that particular Passover on which he died was on a Friday, not a Saturday.