The bottom line of my answer is that John is factually accurate and that he intentionally deviated from the Synoptics for the purpose of noting important theological meaning, not for the sake of dating accuracy itself.
There are two possible chronologies, which I will call C14 and C15.
C14: Crucifixion on 14 Nisan. It implies, with Nisan dates reckoned as per the Jewish official calendar:
- 13 Nisan: from Wed. sunset to Thursday sunset.
- 14 Nisan: from Thursday sunset to Friday sunset.
- 15 Nisan: from Friday sunset to Saturday sunset (regular weekly Sabbath).
- The Last Supper was held one day before the time of the Passover meal according to the Jewish official calendar.
- Jesus died when the Paschal lambs where being sacrificed in the Temple.
- The information about dates provided by John is factually accurate, while that provided by the Synoptics is not.
C15: Crucifixion on 15 Nisan. It implies, with Nisan dates reckoned as per the Jewish official calendar:
- 14 Nisan: from Wed. sunset to Thursday sunset.
- 15 Nisan: from Thursday sunset to Friday sunset.
- 16 Nisan: from Friday sunset to Saturday sunset (regular weekly Sabbath).
- The Last Supper was held at the time of the Passover meal according to the Jewish official calendar.
- The information about dates provided by the Synoptics is factually accurate, while that provided by John either is not accurate or requires heavy hermeneutic work to make it compatible with the Synoptics.
Whereas two detailed answers to a similar question in hermeneutics.stackexchange.com, by Jas 3.1 and Joseph, argue for C15, I will argue for C14. Specifically, I will argue that there is some key information in John, not taken into account in previous answers, which cannot be made compatible with C15.
First of all, for the purpose of this discussion I will assume an agnostic position about the year of the Crucifixion, as the issue of the Crucifixion being either on Friday April 7, 30 AD or on Friday April 3, 33 AD is wholly irrelevant to the subject of this discussion.
I will assume as an agreed starting point that when Jews refer to a specific date as "the Passover" they mean 15 Nisan, so that when they date an event as occurring "six days before the Passover" they mean that the event occurred on 9 Nisan. This is key for my argument because John dates a specific event that way: the supper that Lazarus and his sisters Mary and Martha made for Jesus in Bethany, during the course of which Mary anointed Jesus:
Jesus, therefore, six days before the Passover, came to Bethany
where Lazarus was, whom Jesus had raised from the dead. So they made
Him a supper there, and Martha was serving; but Lazarus was one of
those reclining at the table with Him. Mary then took a pound of very
costly perfume of pure nard, and anointed the feet of Jesus and wiped
His feet with her hair; and the house was filled with the fragrance of
the perfume. But Judas Iscariot, one of His disciples, who was
intending to betray Him, said, “Why was this perfume not sold for
three hundred denarii and given to poor people?” Now he said this, not
because he was concerned about the poor, but because he was a thief,
and as he had the money box, he used to pilfer what was put into it.
Therefore Jesus said, “Let her alone, so that she may keep it for the
day of My burial. For you always have the poor with you, but you do
not always have Me.”
The large crowd of the Jews then learned that He was there; and they
came, not for Jesus’ sake only, but that they might also see Lazarus,
whom He raised from the dead. (John 12:1-9. NASB.)
Now, lets reckon the day of week of that supper in both possible chronologies working backwards:
C14:
- 15 Nisan: from Friday sunset to Saturday sunset (regular weekly Sabbath).
- 14 Nisan: from Thursday sunset to Friday sunset.
- 13 Nisan: from Wed. sunset to Thursday sunset.
- 12 Nisan: from Tuesday sunset to Wed. sunset.
- 11 Nisan: from Monday sunset to Tuesday sunset.
- 10 Nisan: from Sunday sunset to Monday sunset.
- 09 Nisan: from Saturday sunset to Sunday sunset.
In this chronology, the event is perfectly compatible with Sabbath observance for both the hosts of the supper and "the large crowd of the Jews" that went from Jerusalem to Bethany to see Jesus and Lazarus.
C15:
- 16 Nisan: from Friday sunset to Saturday sunset (regular weekly Sabbath).
- 15 Nisan: from Thursday sunset to Friday sunset.
- 14 Nisan: from Wed. sunset to Thursday sunset.
- 13 Nisan: from Tuesday sunset to Wed. sunset.
- 12 Nisan: from Monday sunset to Tuesday sunset.
- 11 Nisan: from Sunday sunset to Monday sunset.
- 10 Nisan: from Saturday sunset to Sunday sunset.
- 09 Nisan: from Friday sunset to Saturday sunset (regular weekly Sabbath).
In this chronology, the event is wholly incompatible with Sabbath observance for both the hosts of the supper and "the large crowd of the Jews" that went from Jerusalem to Bethany to see Jesus and Lazarus, as the distance from Jerusalem to Bethany exceeds what Jews are allowed to travel on a Sabbath.
Since I stated the teleological side of my argument, i.e. the reason why John intentionally deviated from the Synoptics, as the purpose of noting important theological meaning, and as the straightforward theological meaning in C14 and not in C15 is that in the former Jesus died when the paschal lambs where being sacrificed in the Temple, my argument would be strengthened if I could show that John provides another chronological coincidence between the paschal lambs and Jesus. And indeed he does.
Let's quote John's narrative of Jesus' entrance to Jerusalem, which follows right after the supper in Bethany:
On the next day the large crowd who had come to the feast, when they
heard that Jesus was coming to Jerusalem, took the branches of the
palm trees and went out to meet Him, and began to shout, “Hosanna!
BLESSED IS HE WHO COMES IN THE NAME OF THE LORD, even the King of
Israel.” Jesus, finding a young donkey, sat on it; as it is written,
“FEAR NOT, DAUGHTER OF ZION; BEHOLD, YOUR KING IS COMING, SEATED ON A
DONKEY’S COLT.” (John 12:12-15. NASB.)
Thus, Jesus entered Jerusalem on 10 Nisan. Let's read now the instructions in Exodus for the preparation of the paschal lamb:
Now the LORD said to Moses and Aaron in the land of Egypt, “This month
shall be the beginning of months for you; it is to be the first month
of the year to you. Speak to all the congregation of Israel, saying,
‘On the tenth of this month they are each one to take a lamb for
themselves, according to their fathers’ households, a lamb for each
household. Now if the household is too small for a lamb, then he and
his neighbor nearest to his house are to take one according to the
number of persons in them; according to what each man should eat, you
are to divide the lamb. Your lamb shall be an unblemished male a year
old; you may take it from the sheep or from the goats. You shall keep
it until the fourteenth day of the same month, then the whole assembly
of the congregation of Israel is to kill it at twilight. (Exodus
12:1-6)
Thus, on 10 Nisan the large number of lambs that were being kept grazing in the fields around Jerusalem for the feast were brought into the city so that each household could buy one for themselves. Therefore, Jesus entered Jerusalem at the same time as the paschal lambs were entering the city.