Short Answer: Yes, it is definitely possible for John's chronology to be reconciled with that of the Synoptics. As the following chart shows, the sequence of Passion events recorded in John is in perfect harmony with the sequence in the Synoptics. When John's terminology is properly understood, it becomes clear that John's chronology does not contradict that of the Synoptics, but actually strengthens and adds further clarity to it -- particularly for the audience he was writing to.
The difficulty is not in the sequence of events, but in properly understanding the terms John used to locate those events in time. The key to understanding John's choice of terms lies in the historical context of the Gospel.
Historical Context of the Gospel of John
Audience: The best we can tell, John probably wrote his Gospel somewhere around 85 AD in Asia -- probably Ephesus.1 We can get a bit more specific about his audience by examining literary clues:
John explained Jewish customs, translated Jewish names, and located Palestinian sites. These facts suggest that he was writing for Gentile readers who lived primarily outside Palestine.2
Of course, Rome ruled the land in those days, so John would have had to translate much of this Jewish material before his Gentile ("Roman") audience could understand it.
Relationship to the Synoptics: As mentioned in the question, there is strong evidence that both John and his intended audience were intimately familiar with the Synoptic tradition. John's Gospel was thus supplementary in nature, written for a theological purpose, rather than to rehash the historical details they were all already familiar with. This is why John doesn't spend his time rehashing Jesus' genealogy, birth, baptism, temptation, calling of the twelve, exercising demons, parables, transfiguration, agony in Gesthemane, ascension, etc. In fact, it is estimated that 93% of the material in John is unique to John.3
He focused on Jesus' ministry in Jerusalem, the Jewish feasts, Jesus'
private conversations with individuals, and His preparation of His disciples.4
This verse indicates the Jews feared that they might be defiled, and thus precluded from eating the Passover. The semantic range of the term "the Passover" includes "the Feast of Unleavened Bread", as seen elsewhere in Scripture:
Now the Feast of Unleavened Bread, which is called the Passover, was approaching. -Luke 22:1
This view is supported by both modern commentators and ancient Jewish sources. For example, one esteemed commentator (citing the Mishnah) recently explained:
The "Passover" was the name that the Jews used to describe both the Passover proper, and the entire festival that followed it, which included the Feast of Unleavened Bread . . . Part of the feast was the offering of two peace offerings, called the Chagigah—one on the Nisan 14 and one on Nisan 15, the latter being the first day of the Feast of Unleavened Bread. Jewish law was very strict that no one who was defiled could offer the Chagigah.5
Thus, John 18:28 seems to simply be indicating that the Jews were concerned that they would not be able to eat the Feast / offer the Chagigah.
Why did John use the term "the Passover", rather than "the Feast"? Probably to highlight the irony of the situation: the Jews go to great lengths to preserve their participation in the Passover Feast while, at the same time, going to great lengths to betray the True Passover.
The beginning of the verse says that it was now "the day of preparation of the Passover." The term "the day of preparation" is a single word in Greek (παρασκευὴ) that normally referred to "Friday" (which is the day of preparation for "Saturday," the Sabbath.)6 In John's day, παρασκευὴ had become the colloquial name of the 6th day of the week. 7 So, the most natural rendition of the statement would be "the Friday of the Passover."
Given that this is the preferred interpretation exegetically, and that it aligns perfectly with the chronology of John, as well as the Synoptic witnesses, there is no reason to suspect that it means anything different. This apparent contradiction only exists in modern English.
Why did John use the term "the day of preparation" of the Passover? Probably to help his readers understand the Jews' request to break the legs of the condemned in verses 31-36; they couldn't have people hanging on crosses on that Sabbath, "for the day of that Sabbath was great" (being associated with the Passover.) Again we see the irony of the Jews' high view of the Passover festival, and disregard for the True Passover.
The verse goes on to specify that "it was about the sixth hour" when Pilate brought Jesus out and told the Jews "Behold, your King!" The important question to answer here is: by which clock? At the time of the writing of the Gospel of John the Romans were using a system of reckoning time which would have placed "the sixth hour" at about 6:00 AM,8 as evidenced by recovered Roman legal documents.9 So, was John using the Jewish calendar, the Roman legal calendar, or did he just goof up on a very specific timestamp?
There are a number of reasons to favor the view that John was using the Roman legal calendar here:
Recall that John's late-century, Gentile audience was most likely more Roman than Jewish in culture, and so it is likely that the term "the sixth hour" would mean 6:00 AM to them -- especially in reference to Roman legal matters.
Recall that John and his readers were already familiar with the Synoptic tradition. It would be very odd for John to blatantly contradict that tradition with no explanation. (It would be even more odd for John to accidentally make such a specific mistake!)
Recall that most of John' material served to supplement the Synoptic tradition. The idea of John adding a "Roman legal" timestamp to clarify the timing of this event for his readers is highly consistent with the nature of this Gospel.
"The sixth hour" (by the Roman legal calendar) was the exact time at which the Romans typically began their legal work.10 Given the haste of the Jews in capturing Jesus and bringing Him to Pilot, and the fact that Jesus was captured in the middle of the night, it makes perfect sense for them to get him to Pilot first thing in the morning -- and for John to highlight this!
This would not be the first time that John's Gospel displayed a more "Roman" focus than the Synoptics. In fact, we have another example in the very next verse:
The chief priests answered, "We have no king but Caesar." -John 19:15
This reference to Caesar only appears in John.
- If John was using the Roman legal calendar, John's Passion chronology aligns perfectly with that of the Synoptics (refer to chart.) We're not talking about a solution that makes it possible to reconcile the accounts, we are looking at a legitimate, historically-vetted definition of the term that fits exactly with everything else we know about the Passion chronology.
Why did John use the term "the sixth hour" to refer to 6:00 AM? Because that was the term his audience would have been familiar with in regards to Roman legal matters, and being the start of the Roman legal workday, it highlighted the Jews' haste in driving Pilot to sentence Jesus first thing in the morning.
1: D. A. Carson, The Gospel According to John, The Pillar New Testament Commentary (Grand Rapids: Eerdmans, 1991, 82-87; Dr. Thomas L. Constable, Notes on John: 2013 Edition, http://www.soniclight.com/constable/notes.htm (accessed February 6, 2013), 2-3
2: Constable, 6
3: Constable, 4 citing Edwin A. Blum, "John." In Bible Knowledge Commentary: New Testament, 267-348, Edited by John F. Walvoord and Roy B. Zuck (Wheaton: Scripture Press Publications, Victor Books, 1983), 269
4: Constable, 4
5: Constable, 281 citing Pesahim 6:3 from The Mishnah. Translated by Herbert Danby (London: Oxford University Press, 1933) . . . cf. Flavius Josephus, The Works of Flavius Josephus, Translated by William Whiston (London: T. Nelson and Sons, 1866); reprint ed. Peabody, Mass.: (Hendrickson Publishers, 1988), 14:2:1; 17:9:3; See also Carson, 589-590
6: Carson, 603 citing Charles C Torrey, "The Date of the Crucifixion According to the Fourth Gospel", Journal of Biblical Literature, 50:4 (1931), 241; A. J. B. Higgins, "The Origins of the Eucharist", New Testament Studies 1 (1954-55), 206ff; Leon Morris, The Gospel According to John, New International Commentary on the New Testament series (Grand Rapids: Wm. B. Eerdmans Publishing Co., 1971), 776-777
7: Constable, 292 citing Torrey, 241; Higgins, 206-8; B. F. Westcott, The Gospel According to St. John: The Authorised Version with Introduction and Notes (London: James Clarke & Co., Ltd., 1958), 1:343; Harold W. Hoehner, Chronological Aspects of the Life of Christ, Contemporary Evangelical Perspectives series (Grand Rapids: Zondervan Publishing House, 1977), 70
8: Constable, citing Westcott, 2:324-26; and R. V. G. Tasker, The Gospel According to St. John: An Introduction and Commentary, Tyndale New Testament Commentaries series (Grand Rapids: Wm. B. Eerdmans Publishing Co., 1960), 209
9: Constable, citing Morris, 708
10: Constable, citing A. N. Sherwin-White, Roman Society and Roman Law in the New Testament (Oxford: Oxford University Press, 1963), 45